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Petrunin, Anton Mikhailovich

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Author ID: petrunin.anton Recent zbMATH articles by "Petrunin, Anton Mikhailovich"
Published as: Petrunin, A.; Petrunin, A. M.; Petrunin, Anton
Homepage: https://anton-petrunin.github.io/
External Links: MGP · Math-Net.Ru · MathOverflow · ORCID · dblp
Documents Indexed: 41 Publications since 1992, including 1 Book

Publications by Year

Citations contained in zbMATH Open

32 Publications have been cited 305 times in 227 Documents Cited by Year
Semiconcave functions in Alexandrov’s geometry. Zbl 1166.53001
Petrunin, Anton
56
2007
Alexandrov meets Lott-Villani-Sturm. Zbl 1247.53038
Petrunin, Anton
41
2011
Parallel transportation for Alexandrov space with curvature bounded below. Zbl 0903.53045
Petrunin, A.
28
1998
Diffeomorphism finiteness, positive pinching, and second homotopy. Zbl 0941.53026
Petrunin, A.; Tuschmann, W.
19
1999
Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces. Zbl 1192.53040
Kapovitch, Vitali; Petrunin, Anton; Tuschmann, Wilderich
17
2010
Extremal subsets in Aleksandrov spaces and the generalized Liberman theorem. Zbl 0802.53019
Perel’man, G. Ya.; Petrunin, A. M.
17
1993
Harmonic functions on Alexandrov spaces and their applications. Zbl 1071.53527
Petrunin, Anton
16
2003
Alexandrov meets Kirszbraun. Zbl 1251.53046
Alexander, Stephanie; Kapovitch, Vitali; Petrunin, Anton
13
2011
Applications of quasigeodesics and gradient curves. Zbl 0892.53026
Petrunin, Anton
13
1997
An invitation to Alexandrov geometry. CAT(0) spaces. Zbl 1433.53065
Alexander, Stephanie; Kapovitch, Vitali; Petrunin, Anton
11
2019
Non-negative pinching, moduli spaces and bundles with infinitely many souls. Zbl 1102.53020
Kapovitch, Vitali; Petrunin, Anton; Tuschmann, Wilderich
9
2005
Metric minimizing surfaces. Zbl 0916.53032
Petrunin, Anton
8
1999
An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds. Zbl 1200.53040
Alexander, Stephanie; Kapovitch, Vitali; Petrunin, Anton
7
2008
Asymptotical flatness and cone structure at infinity. Zbl 1004.53026
Petrunin, Anton; Tuschmann, Wilderich
7
2001
A globalization for non-complete but geodesic spaces. Zbl 1357.53090
Petrunin, Anton
5
2016
Curvature bounded below: a definition a la Berg-Nikolaev. Zbl 1222.53071
Lebedeva, Nina; Petrunin, Anton
5
2010
Telescopic actions. Zbl 1271.57051
Panov, D.; Petrunin, A.
4
2012
On intrinsic isometries to Euclidean space. Zbl 1225.53041
Petrunin, A.
4
2011
An upper bound for the curvature integral. Zbl 1206.53048
Petrunin, A. M.
3
2009
Polyhedral approximations of Riemannian manifolds. Zbl 1034.53070
Petrunin, Anton
3
2003
Collapsing vs. positive pinching. Zbl 0947.53018
Petrunin, A.; Rong, X.; Tuschmann, W.
3
1999
Metric-minimizing surfaces revisited. Zbl 1429.53060
Petrunin, Anton; Stadler, Stephan
2
2019
Bipolar comparison. Zbl 07040588
Lebedeva, Nina; Petrunin, Anton; Zolotov, Vladimir
2
2019
Piecewise distance preserving maps. Zbl 1333.52019
Petrunin, A.; Yashinski, A.
2
2016
Smoothing 3-dimensional polyhedral spaces. Zbl 1346.53040
Shevchishin, Vsevolod; Petrunin, Anton; Matveev, Vladimir; Lebedeva, Nina
2
2015
Sweeping out sectional curvature. Zbl 1296.53091
Panov, Dmitri; Petrunin, Anton
2
2014
Monotonicity of saddle maps. Zbl 1414.53066
Petrunin, Anton; Stadler, Stephan
1
2019
Long geodesics on convex surfaces. Zbl 1431.53042
Akopyan, Arseniy; Petrunin, Anton
1
2018
A quest for 5-point condition of Alexandrov’s type. Zbl 1381.51004
Petrunin, A.
1
2018
On the total curvature of minimizing geodesics on convex surfaces. Zbl 1387.53011
Lebedeva, N.; Petrunin, A.
1
2018
Ramification conjecture and Hirzebruch’s property of line arrangements. Zbl 1376.51007
Panov, D.; Petrunin, A.
1
2016
Local characterization of polyhedral spaces. Zbl 1333.52018
Lebedeva, Nina; Petrunin, Anton
1
2015
An invitation to Alexandrov geometry. CAT(0) spaces. Zbl 1433.53065
Alexander, Stephanie; Kapovitch, Vitali; Petrunin, Anton
11
2019
Metric-minimizing surfaces revisited. Zbl 1429.53060
Petrunin, Anton; Stadler, Stephan
2
2019
Bipolar comparison. Zbl 07040588
Lebedeva, Nina; Petrunin, Anton; Zolotov, Vladimir
2
2019
Monotonicity of saddle maps. Zbl 1414.53066
Petrunin, Anton; Stadler, Stephan
1
2019
Long geodesics on convex surfaces. Zbl 1431.53042
Akopyan, Arseniy; Petrunin, Anton
1
2018
A quest for 5-point condition of Alexandrov’s type. Zbl 1381.51004
Petrunin, A.
1
2018
On the total curvature of minimizing geodesics on convex surfaces. Zbl 1387.53011
Lebedeva, N.; Petrunin, A.
1
2018
A globalization for non-complete but geodesic spaces. Zbl 1357.53090
Petrunin, Anton
5
2016
Piecewise distance preserving maps. Zbl 1333.52019
Petrunin, A.; Yashinski, A.
2
2016
Ramification conjecture and Hirzebruch’s property of line arrangements. Zbl 1376.51007
Panov, D.; Petrunin, A.
1
2016
Smoothing 3-dimensional polyhedral spaces. Zbl 1346.53040
Shevchishin, Vsevolod; Petrunin, Anton; Matveev, Vladimir; Lebedeva, Nina
2
2015
Local characterization of polyhedral spaces. Zbl 1333.52018
Lebedeva, Nina; Petrunin, Anton
1
2015
Sweeping out sectional curvature. Zbl 1296.53091
Panov, Dmitri; Petrunin, Anton
2
2014
Telescopic actions. Zbl 1271.57051
Panov, D.; Petrunin, A.
4
2012
Alexandrov meets Lott-Villani-Sturm. Zbl 1247.53038
Petrunin, Anton
41
2011
Alexandrov meets Kirszbraun. Zbl 1251.53046
Alexander, Stephanie; Kapovitch, Vitali; Petrunin, Anton
13
2011
On intrinsic isometries to Euclidean space. Zbl 1225.53041
Petrunin, A.
4
2011
Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces. Zbl 1192.53040
Kapovitch, Vitali; Petrunin, Anton; Tuschmann, Wilderich
17
2010
Curvature bounded below: a definition a la Berg-Nikolaev. Zbl 1222.53071
Lebedeva, Nina; Petrunin, Anton
5
2010
An upper bound for the curvature integral. Zbl 1206.53048
Petrunin, A. M.
3
2009
An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds. Zbl 1200.53040
Alexander, Stephanie; Kapovitch, Vitali; Petrunin, Anton
7
2008
Semiconcave functions in Alexandrov’s geometry. Zbl 1166.53001
Petrunin, Anton
56
2007
Non-negative pinching, moduli spaces and bundles with infinitely many souls. Zbl 1102.53020
Kapovitch, Vitali; Petrunin, Anton; Tuschmann, Wilderich
9
2005
Harmonic functions on Alexandrov spaces and their applications. Zbl 1071.53527
Petrunin, Anton
16
2003
Polyhedral approximations of Riemannian manifolds. Zbl 1034.53070
Petrunin, Anton
3
2003
Asymptotical flatness and cone structure at infinity. Zbl 1004.53026
Petrunin, Anton; Tuschmann, Wilderich
7
2001
Diffeomorphism finiteness, positive pinching, and second homotopy. Zbl 0941.53026
Petrunin, A.; Tuschmann, W.
19
1999
Metric minimizing surfaces. Zbl 0916.53032
Petrunin, Anton
8
1999
Collapsing vs. positive pinching. Zbl 0947.53018
Petrunin, A.; Rong, X.; Tuschmann, W.
3
1999
Parallel transportation for Alexandrov space with curvature bounded below. Zbl 0903.53045
Petrunin, A.
28
1998
Applications of quasigeodesics and gradient curves. Zbl 0892.53026
Petrunin, Anton
13
1997
Extremal subsets in Aleksandrov spaces and the generalized Liberman theorem. Zbl 0802.53019
Perel’man, G. Ya.; Petrunin, A. M.
17
1993
all top 5

Cited by 228 Authors

19 Petrunin, Anton Mikhailovich
12 Lytchak, Alexander
8 Gigli, Nicola
8 Tuschmann, Wilderich
7 Ambrosio, Luigi
7 Kapovitch, Vitali
7 Rong, Xiaochun
7 Zhang, Huichun
6 Alexander, Stephanie B.
6 Lebedeva, Nina V.
5 Grove, Karsten
5 Huang, Jiacheng
5 Mitsuishi, Ayato
5 Panov, Dmitri Alekseevich
5 Stadler, Stephan
4 Bishop, Richard L.
4 Chazal, Frédéric
4 Galaz-Garcia, Fernando
4 Gromov, Mikhael Leonidovich
4 Ketterer, Christian
4 Lott, John
4 Wilking, Burkhard
4 Yamaguchi, Takao
3 Belegradek, Igor
3 Cohen-Steiner, David
3 Dessai, Anand Naique
3 Erbar, Matthias
3 Ge, Jian
3 Gorodski, Claudio
3 Harvey, John Matthew
3 Honda, Shouhei
3 Juillet, Nicolas
3 Kuwada, Kazumasa
3 Li, Nan
3 Mondino, Andrea
3 Searle, Catherine
3 Sturm, Karl-Theodor
3 Xu, Shicheng
3 Yokota, Takumi
3 Zhu, Xiping
2 Amann, Manuel
2 Cao, Jianguo
2 Creutz, Paul
2 Fang, Fuquan
2 Fillastre, François
2 Funano, Kei
2 Gimeno, Vicent
2 Guijarro, Luis
2 Hermann, Martin
2 Herrera, Haydeé
2 Hua, Bobo
2 Jiang, Renjin
2 Jiang, Yin
2 Jiao, Zhenhua
2 Kapovich, Michael
2 Li, Xueping
2 Mérigot, Quentin
2 Munn, Michael
2 Naber, Aaron C.
2 Naor, Assaf
2 Ohta, Shin-ichi
2 Oprea, John F.
2 Savaré, Giuseppe
2 Semola, Daniele
2 Shioya, Takashi
2 Verbitsky, Misha
2 Wenger, Stefan
2 Wraith, David J.
2 Zolotov, Vladimir
1 Ahidar-Coutrix, A.
1 Akopyan, Arseniy V.
1 Albano, Paolo
1 Alesker, Semyon
1 Anderson, Michael T.
1 Andoni, Alexandr
1 Bacher, Kathrin
1 Bamler, Richard H.
1 Bertrand, Jérôme
1 Biau, Gérard
1 Boroński, Jan P.
1 Magalhães Brandão, Maria Cristiane
1 Breuillard, Emmanuel
1 Bruè, Elia
1 Cabezas-Rivas, Esther
1 Cai, Qingsong
1 Caillerie, Claire
1 Cannarsa, Piermarco
1 Cavalletti, Fabio
1 Chen, Binglong
1 Chen, Xiaoyang
1 Colding, Tobias Holck
1 Dahl, Jonathan
1 Dai, Bo
1 Daskalopoulos, Georgios D.
1 De Philippis, Guido
1 De Ponti, Nicolò
1 Dedecker, Jérôme
1 Deng, Jialong
1 Deng, Qintao
1 Deng, Yuxing
...and 128 more Authors
all top 5

Cited in 79 Serials

14 Mathematische Zeitschrift
14 Geometry & Topology
10 Mathematische Annalen
10 Frontiers of Mathematics in China
9 Advances in Mathematics
9 Proceedings of the American Mathematical Society
9 The Journal of Geometric Analysis
8 Geometric and Functional Analysis. GAFA
8 Calculus of Variations and Partial Differential Equations
7 Geometriae Dedicata
6 Transactions of the American Mathematical Society
6 St. Petersburg Mathematical Journal
5 Inventiones Mathematicae
4 Journal of Mathematical Analysis and Applications
4 Journal of Functional Analysis
4 Annals of Global Analysis and Geometry
4 Journal de Mathématiques Pures et Appliquées. Neuvième Série
4 Potential Analysis
4 Analysis and Geometry in Metric Spaces
3 Annales de l’Institut Fourier
3 Duke Mathematical Journal
3 Manuscripta Mathematica
3 Revista Matemática Iberoamericana
3 Differential Geometry and its Applications
3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
2 Compositio Mathematica
2 Memoirs of the American Mathematical Society
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Topology and its Applications
2 Discrete & Computational Geometry
2 Boletín de la Sociedad Matemática Mexicana. Third Series
2 Electronic Research Announcements of the American Mathematical Society
2 Annals of Mathematics. Second Series
2 Journal of the European Mathematical Society (JEMS)
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Electronic Journal of Statistics
2 Electronic Research Announcements in Mathematical Sciences
2 Journal of Topology and Analysis
1 Archive for Rational Mechanics and Analysis
1 Communications on Pure and Applied Mathematics
1 Indian Journal of Pure & Applied Mathematics
1 Israel Journal of Mathematics
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 The Mathematical Intelligencer
1 Acta Mathematica
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Bulletin of the London Mathematical Society
1 Czechoslovak Mathematical Journal
1 Fuzzy Sets and Systems
1 Illinois Journal of Mathematics
1 Publications Mathématiques
1 Journal of Differential Equations
1 Journal of the Mathematical Society of Japan
1 Journal für die Reine und Angewandte Mathematik
1 Mathematika
1 Monatshefte für Mathematik
1 Osaka Journal of Mathematics
1 Proceedings of the Japan Academy. Series A
1 Tohoku Mathematical Journal. Second Series
1 Chinese Annals of Mathematics. Series B
1 Probability Theory and Related Fields
1 Stochastic Processes and their Applications
1 Bulletin of the American Mathematical Society. New Series
1 Journal of Convex Analysis
1 Electronic Journal of Probability
1 Transformation Groups
1 Conformal Geometry and Dynamics
1 Revista Matemática Complutense
1 Acta Mathematica Sinica. English Series
1 Advances in Geometry
1 Foundations of Computational Mathematics
1 Entropy
1 Central European Journal of Mathematics
1 Oberwolfach Reports
1 Japanese Journal of Mathematics. 3rd Series
1 Arnold Mathematical Journal
1 Journal de l’École Polytechnique – Mathématiques
1 Peking Mathematical Journal

Citations by Year