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Figalli, Alessio

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Author ID: figalli.alessio Recent zbMATH articles by "Figalli, Alessio"
Published as: Figalli, A.; Figalli, Alessio
Homepage: https://people.math.ethz.ch/~afigalli/
External Links: MGP · Math-Net.Ru · Wikidata · ORCID · dblp · GND
Awards: EMS Prize (2012) · Fields Medal (2018)
Documents Indexed: 155 Publications since 2007, including 3 Books
Biographic References: 6 Publications
all top 5

Co-Authors

22 single-authored
17 Ambrosio, Luigi
13 De Philippis, Guido
12 Rifford, Ludovic
11 Maggi, Francesco
7 Colombo, Maria
7 Villani, Cédric
6 Ros-Oton, Xavier
5 Kim, Young-Heon
5 Pratelli, Aldo
4 Bonforte, Matteo
4 Caffarelli, Luis Ángel
4 Jerison, David S.
4 McCann, Robert J.
4 Serra Montolí, Joaquim
4 Valdinoci, Enrico
3 Barrios Barrera, Begoña
3 Carrillo de la Plata, José Antonio
3 Chen, Shibing
3 Ciraolo, Giulio
3 Mooney, Connor
3 Paul, Thierry
3 Shahgholian, Henrik
2 Abbondandolo, Alberto
2 Bernot, Marc
2 Bjorland, Clayton
2 Bourgain, Jean
2 Brézis, Haïm
2 Cabré, Xavier
2 Carlen, Eric Anders
2 Crippa, Gianluca
2 Dipierro, Serena
2 Fathi, Albert
2 Friesecke, Gero
2 Giannoulis, Johannes
2 Gigli, Nicola
2 Guionnet, Alice
2 Jhaveri, Yash
2 Kang, Moon-Jin
2 Laurent, Thomas
2 Pelayo, Alvaro
2 Santambrogio, Filippo
2 Slepčev, Dejan
2 Spinolo, Laura V.
2 Vazquez, Juan Luis
2 Wickramasekera, Neshan
1 Baer, Eric
1 Bekerman, Florent
1 Bench, William
1 Braga, J. Ederson M.
1 Brendle, Simon
1 Cagnetti, Filippo
1 Chang, Sun-Yung Alice
1 Contreras, Gonzalo
1 Cordero-Erausquin, Dario
1 Cozzi, Matteo
1 de Franchis, Carlo
1 Deproit, Laurent
1 Desvillettes, Laurent
1 Di Francesco, Marco
1 Difrancesco, M.
1 Fusco, Nicola
1 Gallouët, Thomas O.
1 Gangbo, Wilfrid
1 Ge, Yuxin
1 Gilles, Sébastien
1 Glaudo, Federico
1 Gomes, Diogo Luís Aguiar
1 Indrei, Emanuel
1 Jerrard, Robert Leon
1 Juillet, Nicolas
1 Klein, Christian
1 Kohn, Robert Vita
1 Krummel, Brian
1 Ligabò, Marilena
1 Loeper, Grégoire
1 Mandorino, Vito
1 Marcon, Diego
1 Markowich, Peter Alexander
1 Millot, Vincent
1 Morales, Javier
1 Moreira, Diego R.
1 Morini, Massimiliano
1 Neumayer, Robin
1 Novaga, Matteo
1 Oh, Byunghyun
1 Palatucci, Giampiero
1 Palmer, Joseph
1 Patacchini, Francesco Saverio
1 Philipowski, Robert
1 Roncoroni, Alberto
1 Runa, Eris
1 Savin, Ovidiu V.
1 Seregin, Gregory A.
1 Sormani, Christina
1 Sparber, Christof
1 Tenne, Adrien
1 Toro, Tatiana
1 Wang, Mu-Tao
1 Webster, Kevin N.
1 Yau, Shing-Tung
...and 1 more Co-Authors
all top 5

Serials

11 Archive for Rational Mechanics and Analysis
11 Communications on Pure and Applied Mathematics
7 Discrete and Continuous Dynamical Systems
6 Journal of Functional Analysis
6 Calculus of Variations and Partial Differential Equations
5 Inventiones Mathematicae
4 Advances in Mathematics
4 Journal de Mathématiques Pures et Appliquées. Neuvième Série
4 SIAM Journal on Mathematical Analysis
4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
3 Communications in Mathematical Physics
3 Duke Mathematical Journal
3 Journal of Differential Equations
3 Journal für die Reine und Angewandte Mathematik
3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
3 Communications in Partial Differential Equations
3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
3 Journal of the European Mathematical Society (JEMS)
3 Analysis & PDE
2 Acta Mathematica
2 American Journal of Mathematics
2 Publications Mathématiques
2 Mathematische Annalen
2 Proceedings of the American Mathematical Society
2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 Geometric and Functional Analysis. GAFA
2 Bulletin of the American Mathematical Society. New Series
2 Methods and Applications of Analysis
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Oberwolfach Reports
1 Israel Journal of Mathematics
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Gazette des Mathématiciens
1 Indiana University Mathematics Journal
1 Journal of Differential Geometry
1 Journal of Economic Theory
1 Mathematische Zeitschrift
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 Rendiconti del Seminario Matematico della Università di Padova
1 Tohoku Mathematical Journal. Second Series
1 Transactions of the American Mathematical Society
1 Chinese Annals of Mathematics. Series B
1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
1 Differential and Integral Equations
1 Differential Geometry and its Applications
1 IMRN. International Mathematics Research Notices
1 The Journal of Geometric Analysis
1 Notices of the American Mathematical Society
1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Journal of Mathematical Sciences (New York)
1 Advances in Geometry
1 ALEA. Latin American Journal of Probability and Mathematical Statistics
1 Journal of Fixed Point Theory and Applications
1 Discrete and Continuous Dynamical Systems. Series S
1 Advances in Calculus of Variations
1 Cambridge Journal of Mathematics
1 Philosophical Transactions A. Royal Society of London
1 Bollettino dell’Unione Matematica Italiana
1 Zurich Lectures in Advanced Mathematics

Publications by Year

Citations contained in zbMATH Open

140 Publications have been cited 2,010 times in 1,273 Documents Cited by Year
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations. Zbl 1215.35045
Carrillo, J. A.; Difrancesco, M.; Figalli, A.; Laurent, T.; Slepčev, D.
110
2011
A mass transportation approach to quantitative isoperimetric inequalities. Zbl 1196.49033
Figalli, A.; Maggi, F.; Pratelli, A.
110
2010
Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients. Zbl 1169.60010
Figalli, Alessio
77
2008
Isoperimetry and stability properties of balls with respect to nonlocal energies. Zbl 1312.49051
Figalli, A.; Fusco, N.; Maggi, F.; Millot, V.; Morini, M.
57
2015
Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces. Zbl 1316.35061
Barrios, Begoña; Figalli, Alessio; Valdinoci, Enrico
48
2014
The Monge-Ampère equation and its applications. Zbl 1435.35003
Figalli, Alessio
43
2017
Non-local gradient dependent operators. Zbl 1252.35099
Bjorland, C.; Caffarelli, L.; Figalli, A.
43
2012
Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278
Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio
42
2012
Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088
Caffarelli, Luis; Figalli, Alessio
41
2013
On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions. Zbl 1156.60036
Ambrosio, Luigi; Figalli, Alessio
39
2009
The Monge-Ampère equation and its link to optimal transportation. Zbl 06377770
De Philippis, Guido; Figalli, Alessio
38
2014
Optimal transportation on non-compact manifolds. Zbl 1198.49044
Fathi, Albert; Figalli, Alessio
34
2010
Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass Keller-Segel equation. Zbl 1307.26027
Carlen, Eric A.; Figalli, Alessio
33
2013
A refined Brunn-Minkowski inequality for convex sets. Zbl 1192.52015
Figalli, A.; Maggi, F.; Pratelli, A.
32
2009
\(W^{2,1}\) regularity for solutions of the Monge-Ampère equation. Zbl 1286.35107
De Philippis, Guido; Figalli, Alessio
31
2013
The optimal partial transport problem. Zbl 1245.49059
Figalli, Alessio
31
2010
Transport maps for \(\beta\)-matrix models and universality. Zbl 1330.49046
Bekerman, F.; Figalli, A.; Guionnet, A.
29
2015
Asymptotics of the \(s\)-perimeter as \(s \searrow 0\). Zbl 1275.49083
Dipierro, Serena; Figalli, Alessio; Palatucci, Giampiero; Valdinoci, Enrico
28
2013
Mass transportation on sub-Riemannian manifolds. Zbl 1201.49048
Figalli, Alessio; Rifford, Ludovic
28
2010
Continuity of optimal transport maps and convexity of injectivity domains on small deformations of \(\mathbb S^2\). Zbl 1175.49040
Figalli, Alessio; Rifford, Ludovic
27
2009
Regularity and Bernstein-type results for nonlocal minimal surfaces. Zbl 1380.49060
Figalli, Alessio; Valdinoci, Enrico
26
2017
\(C^{1}\) regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two. Zbl 1170.35400
Figalli, Alessio; Loeper, Grégoire
26
2009
Nearly round spheres look convex. Zbl 1241.53031
Figalli, Alessio; Rifford, Ludovic; Villani, Cedric
25
2012
Some new well-posedness results for continuity and transport equations, and applications to the chromatography system. Zbl 1222.35060
Ambrosio, Luigi; Crippa, Gianluca; Figalli, Alessio; Spinolo, Laura V.
24
2009
Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation. Zbl 1286.46035
Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo
23
2013
On the shape of liquid drops and crystals in the small mass regime. Zbl 1279.76005
Figalli, A.; Maggi, F.
23
2011
Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds. Zbl 1262.58013
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
23
2011
When is multidimensional screening a convex program? Zbl 1282.90085
Figalli, Alessio; Kim, Young-Heon; McCann, Robert J.
23
2011
Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data. Zbl 1231.35186
Ambrosio, Luigi; Figalli, Alessio; Friesecke, Gero; Giannoulis, Johannes; Paul, Thierry
22
2011
Strongly nonlocal dislocation dynamics in crystals. Zbl 1304.35731
Dipierro, Serena; Figalli, Alessio; Valdinoci, Enrico
21
2014
A note on interior \(W^{2,1+ \varepsilon }\) estimates for the Monge-Ampère equation. Zbl 1280.35153
De Philippis, G.; Figalli, A.; Savin, O.
21
2013
Hölder continuity and injectivity of optimal maps. Zbl 1281.49037
Figalli, Alessio; Kim, Young-Heon; McCann, Robert J.
20
2013
A sharp stability result for the relative isoperimetric inequality inside convex cones. Zbl 1262.49045
Figalli, A.; Indrei, E.
20
2013
On the Ma-Trudinger-Wang curvature on surfaces. Zbl 1203.53034
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
20
2010
A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions. Zbl 1203.35126
Figalli, Alessio; Gigli, Nicola
20
2010
Geodesics in the space of measure-preserving maps and plans. Zbl 1253.76007
Ambrosio, Luigi; Figalli, Alessio
20
2009
A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment. Zbl 1405.35206
Figalli, Alessio; Kang, Moon-Jin
18
2019
Quantitative stability for the Brunn-Minkowski inequality. Zbl 1380.52010
Figalli, Alessio; Jerison, David
18
2017
On the Hausdorff dimension of the Mather quotient. Zbl 1172.37018
Fathi, Albert; Rifford, Ludovic; Figalli, Alessio
18
2009
Regularity of optimal transport maps on multiple products of spheres. Zbl 1268.49053
Figalli, Alessio; Kim, Young-Heon; McCann, Robert J.
17
2013
Existence of Eulerian solutions to the semigeostrophic equations in physical space: The 2-dimensional periodic case. Zbl 1258.35164
Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio
17
2012
Confinement in nonlocal interaction equations. Zbl 1233.35032
Carrillo, J. A.; Di Francesco, M.; Figalli, A.; Laurent, T.; Slepčev, D.
17
2012
Global regularity for the free boundary in the obstacle problem for the fractional Laplacian. Zbl 1409.35044
Barrios, Begoña; Figalli, Alessio; Ros-Oton, Xavier
16
2018
Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. Zbl 1411.53030
Ciraolo, Giulio; Figalli, Alessio; Maggi, Francesco; Novaga, Matteo
16
2018
On the isoperimetric problem for radial log-convex densities. Zbl 1307.49046
Figalli, A.; Maggi, F.
16
2013
Partial regularity of Brenier solutions of the Monge-Ampère equation. Zbl 1193.35087
Figalli, Alessio; Kim, Young-Heon
16
2010
Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains. Zbl 1377.35259
Bonforte, Matteo; Figalli, Alessio; Ros-Oton, Xavier
15
2017
BMO-type norms related to the perimeter of sets. Zbl 1352.46026
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio
15
2016
A general class of free boundary problems for fully nonlinear elliptic equations. Zbl 1326.35137
Figalli, Alessio; Shahgholian, Henrik
15
2014
Total variation flow and sign fast diffusion in one dimension. Zbl 1242.35049
Bonforte, Matteo; Figalli, Alessio
15
2012
Regularity properties of optimal maps between nonconvex domains in the plane. Zbl 1193.35086
Figalli, Alessio
15
2010
A simple proof of the Morse-Sard theorem in Sobolev spaces. Zbl 1157.58002
Figalli, Alessio
15
2008
On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations. Zbl 1138.49031
Ambrosio, Luigi; Figalli, Alessio
15
2008
Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains. Zbl 1443.35067
Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis
14
2018
Partial regularity for optimal transport maps. Zbl 1325.49051
De Philippis, Guido; Figalli, Alessio
14
2015
A global existence result for the semigeostrophic equations in three dimensional convex domains. Zbl 1287.35064
Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio
14
2014
Existence and uniqueness of maximal regular flows for non-smooth vector fields. Zbl 1348.34039
Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio
13
2015
Existence, uniqueness, and regularity of optimal transport maps. Zbl 1132.28322
Figalli, Alessio
13
2007
High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces. Zbl 1114.37034
Abbondandolo, Alberto; Figalli, Alessio
13
2007
A note on Cheeger sets. Zbl 1168.39008
Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo
12
2009
Geometry of minimizers for the interaction energy with mildly repulsive potentials. Zbl 1408.49035
Carrillo, J. A.; Figalli, A.; Patacchini, F. S.
11
2017
Quantitative stability for sumsets in \(\mathbb R^n\). Zbl 1325.49052
Figalli, Alessio; Jerison, David
11
2015
Absolute continuity of Wasserstein geodesics in the Heisenberg group. Zbl 1246.53049
Figalli, A.; Juillet, N.
11
2008
Free boundary regularity in the parabolic fractional obstacle problem. Zbl 1420.35428
Barrios, Begoña; Figalli, Alessio; Ros-Oton, Xavier
10
2018
Regularity theory for local and nonlocal minimal surfaces: an overview. Zbl 1385.49028
Cozzi, Matteo; Figalli, Alessio
10
2017
Second order stability for the Monge-Ampère equation and strong Sobolev convergence of optimal transport maps. Zbl 1278.35090
De Philippis, Guido; Figalli, Alessio
10
2013
Local semiconvexity of Kantorovich potentials on non-compact manifolds. Zbl 1228.49047
Figalli, Alessio; Gigli, Nicola
10
2011
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces. Zbl 1228.60063
Ambrosio, Luigi; Figalli, Alessio
10
2011
On stable solutions for boundary reactions: a De Giorgi-type result in dimension \(4 + 1\). Zbl 1441.35254
Figalli, Alessio; Serra, Joaquim
9
2020
Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow. Zbl 1384.35130
Figalli, Alessio; Kang, Moon-Jin; Morales, Javier
9
2018
On the Lagrangian structure of transport equations: the Vlasov-Poisson system. Zbl 1403.35085
Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio
9
2017
Universality in several-matrix models via approximate transport maps. Zbl 1402.60009
Figalli, Alessio; Guionnet, Alice
9
2016
Regularity results for very degenerate elliptic equations. Zbl 1282.35175
Colombo, Maria; Figalli, Alessio
9
2014
Regularity of optimal transport maps (after Ma-Trudinger-Wang and Loeper). Zbl 1211.49054
Figalli, Alessio
9
2010
On flows of \(H ^{3/2}\)-vector fields on the circle. Zbl 1195.46032
Figalli, Alessio
9
2010
On the fine structure of the free boundary for the classical obstacle problem. Zbl 1408.35228
Figalli, Alessio; Serra, Joaquim
8
2019
Generalized solutions for the Euler equations in one and two dimensions. Zbl 1170.35078
Bernot, Marc; Figalli, Alessio; Santambrogio, Filippo
7
2009
An approximation lemma about the cut locus, with applications in optimal transport theory. Zbl 1172.53022
Figalli, Alessio; Villani, Cédric
7
2008
Optimal regularity of the convex envelope. Zbl 1316.49019
De Philippis, Guido; Figalli, Alessio
6
2015
Closing Aubry sets. II. Zbl 1377.37090
Figalli, A.; Rifford, L.
6
2015
Boundary \(\varepsilon\)-regularity in optimal transportation. Zbl 1307.49045
Chen, Shibing; Figalli, Alessio
6
2015
Perimeter of sets and BMO-type norms. Zbl 1316.46026
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haïm; Figalli, Alessio
6
2014
Semiclassical limit for mixed states with singular and rough potentials. Zbl 1264.81177
Figalli, Alessio; Ligabò, Marilena; Paul, Thierry
6
2012
Almost everywhere well-posedness of continuity equations with measure initial data. Zbl 1195.35202
Ambrosio, Luigi; Figalli, Alessio
6
2010
A note on the regularity of the free boundaries in the optimal partial transport problem. Zbl 1183.35277
Figalli, Alessio
6
2009
Synchronized traffic plans and stability of optima. Zbl 1148.49039
Bernot, Marc; Figalli, Alessio
6
2008
Symmetry results for critical anisotropic \(p\)-Laplacian equations in convex cones. Zbl 1453.35104
Ciraolo, Giulio; Figalli, Alessio; Roncoroni, Alberto
5
2020
Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations. Zbl 1392.35144
Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis
5
2018
Rigidity and stability of Caffarelli’s log-concave perturbation theorem. Zbl 1359.60050
De Philippis, Guido; Figalli, Alessio
5
2017
Sobolev regularity for Monge-Ampère type equations. Zbl 1271.49031
De Philippis, Guido; Figalli, Alessio
5
2013
On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces. Zbl 1282.28002
Ambrosio, Luigi; Figalli, Alessio; Runa, Eris
5
2013
Convergence to the viscous porous medium equation and propagation of chaos. Zbl 1180.35592
Figalli, Alessio; Philipowski, Robert
5
2008
Optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations. Zbl 07046610
Braga, J. Ederson M.; Figalli, Alessio; Moreira, Diego
4
2019
Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume. Zbl 1369.49065
Figalli, Alessio; Jerison, David
4
2017
Characterization of isoperimetric sets inside almost-convex cones. Zbl 1355.49035
Figalli, Alessio; Baer, Eric
4
2017
An overview of unconstrained free boundary problems. Zbl 1353.35322
Figalli, Alessio; Shahgholian, Henrik
4
2015
Generic hyperbolicity of aubry sets on surfaces. Zbl 1352.37169
Contreras, G.; Figalli, A.; Rifford, L.
4
2015
Closing Aubry sets. I. Zbl 1321.37061
Figalli, A.; Rifford, L.
4
2015
WKB analysis of Bohmian dynamics. Zbl 1341.35139
Figalli, A.; Klein, C.; Markowich, P.; Sparber, C.
4
2014
On supporting hyperplanes to convex bodies. Zbl 1288.52001
Figalli, Alessio; Kim, Young-Heon; McCann, Robert J.
4
2013
On stable solutions for boundary reactions: a De Giorgi-type result in dimension \(4 + 1\). Zbl 1441.35254
Figalli, Alessio; Serra, Joaquim
9
2020
Symmetry results for critical anisotropic \(p\)-Laplacian equations in convex cones. Zbl 1453.35104
Ciraolo, Giulio; Figalli, Alessio; Roncoroni, Alberto
5
2020
Stable solutions to semilinear elliptic equations are smooth up to dimension \(9\). Zbl 07335065
Cabré, Xavier; Figalli, Alessio; Ros-Oton, Xavier; Serra, Joaquim
2
2020
Generic regularity of free boundaries for the obstacle problem. Zbl 1456.35234
Figalli, Alessio; Ros-Oton, Xavier; Serra, Joaquim
1
2020
Optimal regularity and structure of the free boundary for minimizers in cohesive zone models. Zbl 1442.49005
Caffarelli, L.; Cagnetti, F.; Figalli, A.
1
2020
A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment. Zbl 1405.35206
Figalli, Alessio; Kang, Moon-Jin
18
2019
On the fine structure of the free boundary for the classical obstacle problem. Zbl 1408.35228
Figalli, Alessio; Serra, Joaquim
8
2019
Optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations. Zbl 07046610
Braga, J. Ederson M.; Figalli, Alessio; Moreira, Diego
4
2019
Regularity of monotone transport maps between unbounded domains. Zbl 1448.35188
Cordero-Erausquin, Dario; Figalli, Alessio
3
2019
Gradient stability for the Sobolev inequality: the case \(p\geq 2\). Zbl 1417.46023
Figalli, Alessio; Neumayer, Robin
2
2019
Global regularity for the free boundary in the obstacle problem for the fractional Laplacian. Zbl 1409.35044
Barrios, Begoña; Figalli, Alessio; Ros-Oton, Xavier
16
2018
Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. Zbl 1411.53030
Ciraolo, Giulio; Figalli, Alessio; Maggi, Francesco; Novaga, Matteo
16
2018
Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains. Zbl 1443.35067
Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis
14
2018
Free boundary regularity in the parabolic fractional obstacle problem. Zbl 1420.35428
Barrios, Begoña; Figalli, Alessio; Ros-Oton, Xavier
10
2018
Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow. Zbl 1384.35130
Figalli, Alessio; Kang, Moon-Jin; Morales, Javier
9
2018
Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations. Zbl 1392.35144
Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis
5
2018
A quantitative analysis of metrics on \(\mathbb R^n\) with almost constant positive scalar curvature, with applications to fast diffusion flows. Zbl 1408.53018
Ciraolo, Giulio; Figalli, Alessio; Maggi, Francesco
3
2018
On the continuity of center-outward distribution and quantile functions. Zbl 1433.62132
Figalli, Alessio
3
2018
Symplectic \(G\)-capacities and integrable systems. Zbl 1395.57034
Figalli, Alessio; Palmer, Joseph; Pelayo, Álvaro
3
2018
The sharp quantitative Euclidean concentration inequality. Zbl 1385.39005
Figalli, Alessio; Maggi, Francesco; Mooney, Connor
3
2018
Global existence for the semigeostrophic equations via Sobolev estimates for Monge-Ampère. Zbl 1406.35273
Figalli, Alessio
2
2018
The Monge-Ampère equation and its applications. Zbl 1435.35003
Figalli, Alessio
43
2017
Regularity and Bernstein-type results for nonlocal minimal surfaces. Zbl 1380.49060
Figalli, Alessio; Valdinoci, Enrico
26
2017
Quantitative stability for the Brunn-Minkowski inequality. Zbl 1380.52010
Figalli, Alessio; Jerison, David
18
2017
Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains. Zbl 1377.35259
Bonforte, Matteo; Figalli, Alessio; Ros-Oton, Xavier
15
2017
Geometry of minimizers for the interaction energy with mildly repulsive potentials. Zbl 1408.49035
Carrillo, J. A.; Figalli, A.; Patacchini, F. S.
11
2017
Regularity theory for local and nonlocal minimal surfaces: an overview. Zbl 1385.49028
Cozzi, Matteo; Figalli, Alessio
10
2017
On the Lagrangian structure of transport equations: the Vlasov-Poisson system. Zbl 1403.35085
Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio
9
2017
Rigidity and stability of Caffarelli’s log-concave perturbation theorem. Zbl 1359.60050
De Philippis, Guido; Figalli, Alessio
5
2017
Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume. Zbl 1369.49065
Figalli, Alessio; Jerison, David
4
2017
Characterization of isoperimetric sets inside almost-convex cones. Zbl 1355.49035
Figalli, Alessio; Baer, Eric
4
2017
On the regularity of the free boundary in the \(p\)-Laplacian obstacle problem. Zbl 1387.35631
Figalli, Alessio; Krummel, Brian; Ros-Oton, Xavier
3
2017
Lipschitz changes of variables between perturbations of log-concave measures. Zbl 1383.60006
Colombo, Maria; Figalli, Alessio; Jhaveri, Yash
2
2017
Partial \(W^{2,p}\) regularity for optimal transport maps. Zbl 1364.35058
Chen, Shibing; Figalli, Alessio
1
2017
BMO-type norms related to the perimeter of sets. Zbl 1352.46026
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio
15
2016
Universality in several-matrix models via approximate transport maps. Zbl 1402.60009
Figalli, Alessio; Guionnet, Alice
9
2016
On the density function on moduli spaces of toric 4-manifolds. Zbl 1386.53103
Figalli, Alessio; Pelayo, Álvaro
2
2016
Weak KAM theory for a weakly coupled system of Hamilton-Jacobi equations. Zbl 1355.49023
Figalli, Alessio; Gomes, Diogo; Marcon, Diego
2
2016
Stability results on the smoothness of optimal transport maps with general costs. Zbl 1406.35120
Chen, Shibing; Figalli, Alessio
1
2016
Nonlinear bounds in Hölder spaces for the Monge-Ampère equation. Zbl 1338.35196
Figalli, Alessio; Jhaveri, Yash; Mooney, Connor
1
2016
Isoperimetry and stability properties of balls with respect to nonlocal energies. Zbl 1312.49051
Figalli, A.; Fusco, N.; Maggi, F.; Millot, V.; Morini, M.
57
2015
Transport maps for \(\beta\)-matrix models and universality. Zbl 1330.49046
Bekerman, F.; Figalli, A.; Guionnet, A.
29
2015
Partial regularity for optimal transport maps. Zbl 1325.49051
De Philippis, Guido; Figalli, Alessio
14
2015
Existence and uniqueness of maximal regular flows for non-smooth vector fields. Zbl 1348.34039
Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio
13
2015
Quantitative stability for sumsets in \(\mathbb R^n\). Zbl 1325.49052
Figalli, Alessio; Jerison, David
11
2015
Optimal regularity of the convex envelope. Zbl 1316.49019
De Philippis, Guido; Figalli, Alessio
6
2015
Closing Aubry sets. II. Zbl 1377.37090
Figalli, A.; Rifford, L.
6
2015
Boundary \(\varepsilon\)-regularity in optimal transportation. Zbl 1307.49045
Chen, Shibing; Figalli, Alessio
6
2015
An overview of unconstrained free boundary problems. Zbl 1353.35322
Figalli, Alessio; Shahgholian, Henrik
4
2015
Generic hyperbolicity of aubry sets on surfaces. Zbl 1352.37169
Contreras, G.; Figalli, A.; Rifford, L.
4
2015
Closing Aubry sets. I. Zbl 1321.37061
Figalli, A.; Rifford, L.
4
2015
Stability results for the Brunn-Minkowski inequality. Zbl 1346.49068
Figalli, Alessio
3
2015
A note on the dimension of the singular set in free interface problems. Zbl 1340.49044
De Philippis, Guido; Figalli, Alessio
3
2015
A general class of free boundary problems for fully nonlinear parabolic equations. Zbl 1338.35508
Figalli, Alessio; Shahgholian, Henrik
2
2015
On the convexity of injectivity domains on nonfocal manifolds. Zbl 1320.53038
Figalli, Alessio; Gallouët, Thomas O.; Rifford, Ludovic
1
2015
Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces. Zbl 1316.35061
Barrios, Begoña; Figalli, Alessio; Valdinoci, Enrico
48
2014
The Monge-Ampère equation and its link to optimal transportation. Zbl 06377770
De Philippis, Guido; Figalli, Alessio
38
2014
Strongly nonlocal dislocation dynamics in crystals. Zbl 1304.35731
Dipierro, Serena; Figalli, Alessio; Valdinoci, Enrico
21
2014
A general class of free boundary problems for fully nonlinear elliptic equations. Zbl 1326.35137
Figalli, Alessio; Shahgholian, Henrik
15
2014
A global existence result for the semigeostrophic equations in three dimensional convex domains. Zbl 1287.35064
Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio
14
2014
Regularity results for very degenerate elliptic equations. Zbl 1282.35175
Colombo, Maria; Figalli, Alessio
9
2014
Perimeter of sets and BMO-type norms. Zbl 1316.46026
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haïm; Figalli, Alessio
6
2014
WKB analysis of Bohmian dynamics. Zbl 1341.35139
Figalli, A.; Klein, C.; Markowich, P.; Sparber, C.
4
2014
Quantitative stability results for the Brunn-Minkowski inequality. Zbl 1373.49054
Figalli, Alessio
3
2014
Higher integrability for minimizers of the Mumford-Shah functional. Zbl 1316.49044
De Philippis, Guido; Figalli, Alessio
3
2014
How to recognize convexity of a set from its marginals. Zbl 1294.26022
Figalli, Alessio; Jerison, David
3
2014
Partial regularity results in optimal transportation. Zbl 1323.49023
de Philippis, G.; Figalli, A.
1
2014
A geometric approach to correlation inequalities in the plane. Zbl 1288.60024
Figalli, A.; Maggi, F.; Pratelli, A.
1
2014
An excess-decay result for a class of degenerate elliptic equations. Zbl 1286.35114
Colombo, Maria; Figalli, Alessio
1
2014
Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088
Caffarelli, Luis; Figalli, Alessio
41
2013
Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass Keller-Segel equation. Zbl 1307.26027
Carlen, Eric A.; Figalli, Alessio
33
2013
\(W^{2,1}\) regularity for solutions of the Monge-Ampère equation. Zbl 1286.35107
De Philippis, Guido; Figalli, Alessio
31
2013
Asymptotics of the \(s\)-perimeter as \(s \searrow 0\). Zbl 1275.49083
Dipierro, Serena; Figalli, Alessio; Palatucci, Giampiero; Valdinoci, Enrico
28
2013
Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation. Zbl 1286.46035
Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo
23
2013
A note on interior \(W^{2,1+ \varepsilon }\) estimates for the Monge-Ampère equation. Zbl 1280.35153
De Philippis, G.; Figalli, A.; Savin, O.
21
2013
Hölder continuity and injectivity of optimal maps. Zbl 1281.49037
Figalli, Alessio; Kim, Young-Heon; McCann, Robert J.
20
2013
A sharp stability result for the relative isoperimetric inequality inside convex cones. Zbl 1262.49045
Figalli, A.; Indrei, E.
20
2013
Regularity of optimal transport maps on multiple products of spheres. Zbl 1268.49053
Figalli, Alessio; Kim, Young-Heon; McCann, Robert J.
17
2013
On the isoperimetric problem for radial log-convex densities. Zbl 1307.49046
Figalli, A.; Maggi, F.
16
2013
Second order stability for the Monge-Ampère equation and strong Sobolev convergence of optimal transport maps. Zbl 1278.35090
De Philippis, Guido; Figalli, Alessio
10
2013
Sobolev regularity for Monge-Ampère type equations. Zbl 1271.49031
De Philippis, Guido; Figalli, Alessio
5
2013
On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces. Zbl 1282.28002
Ambrosio, Luigi; Figalli, Alessio; Runa, Eris
5
2013
On supporting hyperplanes to convex bodies. Zbl 1288.52001
Figalli, Alessio; Kim, Young-Heon; McCann, Robert J.
4
2013
Stability in geometric and functional inequalities. Zbl 1364.49059
Figalli, Alessio
2
2013
Aubry sets, Hamilton-Jacobi equations, and the Mañé conjecture. Zbl 1364.37137
Figalli, A.; Rifford, L.
2
2013
Non-local gradient dependent operators. Zbl 1252.35099
Bjorland, C.; Caffarelli, L.; Figalli, A.
43
2012
Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278
Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio
42
2012
Nearly round spheres look convex. Zbl 1241.53031
Figalli, Alessio; Rifford, Ludovic; Villani, Cedric
25
2012
Existence of Eulerian solutions to the semigeostrophic equations in physical space: The 2-dimensional periodic case. Zbl 1258.35164
Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio
17
2012
Confinement in nonlocal interaction equations. Zbl 1233.35032
Carrillo, J. A.; Di Francesco, M.; Figalli, A.; Laurent, T.; Slepčev, D.
17
2012
Total variation flow and sign fast diffusion in one dimension. Zbl 1242.35049
Bonforte, Matteo; Figalli, Alessio
15
2012
Semiclassical limit for mixed states with singular and rough potentials. Zbl 1264.81177
Figalli, Alessio; Ligabò, Marilena; Paul, Thierry
6
2012
Isoperimetric-type inequalities on constant curvature manifolds. Zbl 1250.58008
Figalli, Alessio; Ge, Yuxin
3
2012
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations. Zbl 1215.35045
Carrillo, J. A.; Difrancesco, M.; Figalli, A.; Laurent, T.; Slepčev, D.
110
2011
On the shape of liquid drops and crystals in the small mass regime. Zbl 1279.76005
Figalli, A.; Maggi, F.
23
2011
Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds. Zbl 1262.58013
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
23
2011
When is multidimensional screening a convex program? Zbl 1282.90085
Figalli, Alessio; Kim, Young-Heon; McCann, Robert J.
23
2011
Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data. Zbl 1231.35186
Ambrosio, Luigi; Figalli, Alessio; Friesecke, Gero; Giannoulis, Johannes; Paul, Thierry
22
2011
Local semiconvexity of Kantorovich potentials on non-compact manifolds. Zbl 1228.49047
Figalli, Alessio; Gigli, Nicola
10
2011
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces. Zbl 1228.60063
Ambrosio, Luigi; Figalli, Alessio
10
2011
...and 40 more Documents
all top 5

Cited by 1,457 Authors

81 Figalli, Alessio
45 Valdinoci, Enrico
35 Carrillo de la Plata, José Antonio
24 Dipierro, Serena
21 Röckner, Michael
19 Ambrosio, Luigi
18 Novaga, Matteo
17 Maggi, Francesco
17 Santambrogio, Filippo
16 Fusco, Nicola
16 Rifford, Ludovic
15 Shaposhnikov, Stanislav V.
14 Ros-Oton, Xavier
13 Bogachev, Vladimir Igorevich
13 Savin, Ovidiu V.
12 Luo, Dejun
12 Vauchelet, Nicolas
12 Vazquez, Juan Luis
11 Caffarelli, Luis Ángel
11 Indrei, Emanuel
10 Brasco, Lorenzo
10 Carlier, Guillaume
9 Gigli, Nicola
9 Maldonado, Diego
9 McCann, Robert J.
9 Pratelli, Aldo
8 Ciraolo, Giulio
8 De Philippis, Guido
8 Kitagawa, Jun
8 Rossi, Julio Daniel
8 Wang, Xu-Jia
7 Barrios Barrera, Begoña
7 Chen, Shibing
7 Choi, Young-Pil
7 Cinti, Eleonora
7 Colombo, Maria
7 Fetecau, Razvan C.
7 Flandoli, Franco
7 Goldman, Michael
7 Kim, Young-Heon
7 Lee, Paul W. Y.
7 Neumayer, Robin
7 Serra Montolí, Joaquim
7 Sire, Yannick
7 Topaloglu, Ihsan
7 Villani, Cédric
7 Warma, Mahamadi
6 Böröczky, Karoly jun.
6 Cabré, Xavier
6 Cozzi, Matteo
6 Crippa, Gianluca
6 Da Prato, Giuseppe
6 del Barrio, Eustasio
6 Fall, Mouhamed Moustapha
6 Fathi, Max
6 Guillen, Nestor
6 Jabin, Pierre-Emmanuel
6 James, François
6 Le, Nam Q.
6 Ohta, Shin-ichi
6 Palatucci, Giampiero
6 Patacchini, Francesco Saverio
6 Patrizi, Stefania
6 Paul, Thierry
6 Salani, Paolo
6 Slepčev, Dejan
6 Trevisan, Dario
6 Zhang, Xicheng
5 Balogh, Zoltán M.
5 Bertozzi, Andrea Louise
5 Bonforte, Matteo
5 Cesaroni, Annalisa
5 Cicalese, Marco
5 Craig, Katy
5 Del Pino, Manuel A.
5 Di Francesco, Marco
5 Erdős, László
5 Fang, Shizan
5 Gallouët, Thomas O.
5 Garofalo, Nicola
5 Guionnet, Alice
5 Kristály, Alexandru
5 Kuusi, Tuomo
5 Laurent, Thomas
5 Lindgren, Erik
5 Medina, Maria
5 Mészáros, Alpár Richárd
5 Millot, Vincent
5 Mucha, Piotr Bogusław
5 Pass, Brendan
5 Peyré, Gabriel
5 Serfaty, Sylvia
5 Trudinger, Neil Sidney
5 Velichkov, Bozhidar
5 Yau, Horng-Tzer
4 Baradat, Aymeric
4 Barbu, Viorel
4 Bekerman, Florent
4 Brézis, Haïm
4 Bucur, Claudia
...and 1,357 more Authors
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Cited in 232 Serials

98 Calculus of Variations and Partial Differential Equations
56 Journal of Functional Analysis
54 Archive for Rational Mechanics and Analysis
46 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
39 Advances in Mathematics
37 Journal of Differential Equations
32 Discrete and Continuous Dynamical Systems
31 Journal of Mathematical Analysis and Applications
30 SIAM Journal on Mathematical Analysis
26 Journal de Mathématiques Pures et Appliquées. Neuvième Série
25 Communications in Mathematical Physics
24 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
22 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
17 Communications on Pure and Applied Mathematics
17 Communications in Partial Differential Equations
16 Transactions of the American Mathematical Society
16 Communications on Pure and Applied Analysis
15 Probability Theory and Related Fields
15 The Journal of Geometric Analysis
15 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
13 Journal of the European Mathematical Society (JEMS)
12 Potential Analysis
12 NoDEA. Nonlinear Differential Equations and Applications
11 The Annals of Probability
11 Inventiones Mathematicae
11 Manuscripta Mathematica
11 Mathematische Annalen
11 Bulletin des Sciences Mathématiques
11 Journal of Evolution Equations
11 Comptes Rendus. Mathématique. Académie des Sciences, Paris
10 Annali di Matematica Pura ed Applicata. Serie Quarta
10 Proceedings of the American Mathematical Society
10 Revista Matemática Iberoamericana
10 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
9 Nonlinearity
9 Geometric and Functional Analysis. GAFA
8 Journal für die Reine und Angewandte Mathematik
8 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
8 Advances in Calculus of Variations
7 ZAMP. Zeitschrift für angewandte Mathematik und Physik
7 SIAM Journal on Control and Optimization
7 SIAM Journal on Numerical Analysis
7 Applied Mathematics Letters
7 Interfaces and Free Boundaries
7 Communications in Contemporary Mathematics
7 Science China. Mathematics
7 Bulletin of Mathematical Sciences
6 Duke Mathematical Journal
6 Physica D
6 Journal of Mathematical Sciences (New York)
6 Discrete and Continuous Dynamical Systems. Series S
6 Analysis & PDE
5 Journal d’Analyse Mathématique
5 Journal of Mathematical Physics
5 Journal of Statistical Physics
5 Mathematics of Computation
5 Applied Mathematics and Optimization
5 Mathematische Zeitschrift
5 Numerische Mathematik
5 Chinese Annals of Mathematics. Series B
5 Acta Applicandae Mathematicae
5 SIAM Journal on Applied Dynamical Systems
5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
5 Kinetic and Related Models
5 Stochastic and Partial Differential Equations. Analysis and Computations
4 Archiv der Mathematik
4 Quarterly of Applied Mathematics
4 Ricerche di Matematica
4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
4 Journal of Dynamics and Differential Equations
4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
4 SIAM Journal on Scientific Computing
4 Doklady Mathematics
4 Revista Matemática Complutense
4 Acta Mathematica Sinica. English Series
4 Advanced Nonlinear Studies
3 Israel Journal of Mathematics
3 Journal of Computational Physics
3 Geometriae Dedicata
3 Publications Mathématiques
3 Journal of the Korean Mathematical Society
3 Journal of Optimization Theory and Applications
3 Memoirs of the American Mathematical Society
3 European Journal of Applied Mathematics
3 Bulletin of the American Mathematical Society. New Series
3 Journal of Mathematical Imaging and Vision
3 Journal of Nonlinear Science
3 St. Petersburg Mathematical Journal
3 Electronic Journal of Probability
3 Random Matrices: Theory and Applications
3 Analysis and Mathematical Physics
3 Forum of Mathematics, Sigma
3 Analysis and Geometry in Metric Spaces
3 Annals of PDE
3 Séminaire Laurent Schwartz. EDP et Applications
3 Bollettino dell’Unione Matematica Italiana
2 Computers & Mathematics with Applications
2 Mathematical Methods in the Applied Sciences
2 Journal of Geometry and Physics
2 Indiana University Mathematics Journal
...and 132 more Serials
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Cited in 51 Fields

740 Partial differential equations (35-XX)
371 Calculus of variations and optimal control; optimization (49-XX)
180 Probability theory and stochastic processes (60-XX)
147 Differential geometry (53-XX)
98 Statistical mechanics, structure of matter (82-XX)
93 Functional analysis (46-XX)
90 Real functions (26-XX)
84 Global analysis, analysis on manifolds (58-XX)
80 Numerical analysis (65-XX)
77 Fluid mechanics (76-XX)
73 Operator theory (47-XX)
65 Dynamical systems and ergodic theory (37-XX)
64 Measure and integration (28-XX)
58 Biology and other natural sciences (92-XX)
56 Convex and discrete geometry (52-XX)
35 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
34 Mechanics of particles and systems (70-XX)
34 Operations research, mathematical programming (90-XX)
32 Ordinary differential equations (34-XX)
28 Quantum theory (81-XX)
26 Integral equations (45-XX)
23 Mechanics of deformable solids (74-XX)
19 Linear and multilinear algebra; matrix theory (15-XX)
18 Systems theory; control (93-XX)
16 Harmonic analysis on Euclidean spaces (42-XX)
15 Potential theory (31-XX)
14 Statistics (62-XX)
11 Functions of a complex variable (30-XX)
11 Information and communication theory, circuits (94-XX)
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10 Computer science (68-XX)
9 Difference and functional equations (39-XX)
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6 History and biography (01-XX)
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3 General and overarching topics; collections (00-XX)
3 Manifolds and cell complexes (57-XX)
2 Algebraic geometry (14-XX)
2 Topological groups, Lie groups (22-XX)
1 Number theory (11-XX)
1 Nonassociative rings and algebras (17-XX)
1 Sequences, series, summability (40-XX)
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