## Almgren, Frederick Justin jun.

Compute Distance To:
 Author ID: almgren.frederick-j-jun Published as: Almgren, F. J. jun.; Almgren, Frederick J. jun.; Almgren, Fred; Almgren, F.; Almgren, F. J.; Almgren, Frederic J. jun.; Almgren, Frederick J.; Almgren, Frederick more...less External Links: MacTutor · MGP · Wikidata · GND · IdRef
 Documents Indexed: 64 Publications since 1962, including 5 Books 1 Contribution as Editor Biographic References: 6 Publications Co-Authors: 12 Co-Authors with 32 Joint Publications 469 Co-Co-Authors
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### Co-Authors

 32 single-authored 12 Lieb, Elliott Hershel 7 Taylor, Jean Ellen 4 Allard, William K. 2 Browder, William 2 Simon, Leon Melvin 2 Wang, Lihe 1 Gurtin, Morton Edward 1 Montgomery, Hugh Lowell 1 Rivin, Igor 1 Scheffer, Vladimir 1 Schoen, Richard Melvin 1 Super, Boaz J. 1 Thurston, William Paul
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### Serials

 5 Bulletin of the American Mathematical Society. New Series 5 Annals of Mathematics. Second Series 4 Bulletin of the American Mathematical Society 2 Proceedings of the American Mathematical Society 1 The Mathematical Intelligencer 1 Acta Mathematica 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Journal of Differential Geometry 1 Journal of Functional Analysis 1 Memoirs of the American Mathematical Society 1 SIAM Journal on Control and Optimization 1 Topology 1 Journal of the American Mathematical Society 1 The Journal of Geometric Analysis 1 Fractals 1 Forma 1 Proceedings of Symposia in Pure Mathematics 1 Student Mathematical Library 1 Science
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### Fields

 40 Calculus of variations and optimal control; optimization (49-XX) 22 Differential geometry (53-XX) 16 Global analysis, analysis on manifolds (58-XX) 10 Measure and integration (28-XX) 9 Partial differential equations (35-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Functional analysis (46-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Convex and discrete geometry (52-XX) 3 Mechanics of deformable solids (74-XX) 3 Fluid mechanics (76-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Operator theory (47-XX) 2 Geometry (51-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

50 Publications have been cited 1,161 times in 948 Documents Cited by Year
Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints. Zbl 0327.49043
Almgren, F. J. jun.
1976
Curvature-driven flows: a variational approach. Zbl 0783.35002
Almgren, Fred; Taylor, Jean E.; Wang, Lihe
1993
Some interior regularity theorems for minimal surfaces and an extension of Bernstein’s theorem. Zbl 0146.11905
Almgren, F. J. jun.
1966
Symmetric decreasing rearrangement is sometimes continuous. Zbl 0688.46014
Almgren, Frederick J. jun.; Lieb, Elliott H.
1989
Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure. Zbl 0162.24703
Almgren, F. J. jun.
1968
The homotopy groups of the integral cycle groups. Zbl 0118.18503
Almgren, F. J. jun.
1962
Almgren’s big regularity paper. $$Q$$-valued functions minimizing Dirichlet’s integral and the regularity of area-minimizing rectifiable currents up to codimension 2. Edited by V. Scheffer and Jean E. Taylor. Zbl 0985.49001
Almgren, Frederick J. jun.
2000
Optimal isoperimetric inequalities. Zbl 0585.49030
Almgren, F.
1986
Q valued functions minimizing Dirichlet’s integral and the regularity of area minimizing rectifiable currents up to codimension two. Zbl 0557.49021
Almgren, F. J. jun.
1983
The structure of stationary one dimensional varifolds with positive density. Zbl 0339.49020
Allard, W. K.; Almgren, F. J. jun.
1976
Flat flow is motion by crystalline curvature for curves with crystalline energies. Zbl 0867.58020
Almgren, Fred; Taylor, Jean E.
1995
Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds. Zbl 0673.58013
Almgren, Frederick J. jun.; Lieb, Elliot H.
1988
Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals. Zbl 0386.49030
Schoen, Richard; Simon, Leon; Almgren, F. J.
1978
Plateau’s problem. An invitation to varifold geometry. Zbl 0165.13201
Almgren, F. J. jun.
1966
On the radial behavior of minimal surfaces and the uniqueness of their tangent cones. Zbl 0437.53045
Allard, William K.; Almgren, Frederick J. jun.
1981
Co-area, liquid crystals, and minimal surfaces. Zbl 0645.58015
Almgren, F.; Browder, W.; Lieb, E. H.
1988
Mathematical existence of crystal growth with Gibbs-Thomson curvature effects. Zbl 0981.74041
Almgren, Fred; Wang, Lihe
2000
Existence of embedded solutions of Plateau’s problem. Zbl 0417.49051
Almgren, Frederick J. jun.; Simon, Leon
1979
Q valued functions minimizing Dirichlet’s integral and the regularity of area minimizing rectifiable currents up to codimension two. Zbl 0529.49021
Almgren, F. J. jun.
1983
Examples of unknotted curves which bound only surfaces of high genus within their convex hulls. Zbl 0353.53001
Almgren, Frederick J. jun.; Thurston, William P.
1977
Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints. Zbl 0297.49041
Almgren, F. J. jun.
1975
The mean curvature integral is invariant under bending. Zbl 0914.53007
Almgren, Frederic J. jun.; Rivin, Igor
1998
Dirichlet’s problem for multiple valued functions and the regularity of mass minimizing integral currents. Zbl 0439.49028
Almgren, Frederick J. jun.
1979
Three theorems on manifolds with bounded mean curvature. Zbl 0131.19604
Almgren, F. J. jun.
1965
Measure theoretic geometry and elliptic variational problems. Zbl 0185.35202
Almgren, F. J. jun.
1969
Deformations and multiple-valued functions. Zbl 0595.49028
Almgren, F.
1986
Optimal geometry in equilibrium and growth. Zbl 0885.58015
Almgren, Fred; Taylor, Jean E.
1995
Soap bubble clusters. Zbl 1017.49502
Almgren, Fred; Taylor, Jean E.
1996
Optimal isoperimetric inequalities. Zbl 0572.49022
Almgren, F.
1985
Symmetric decreasing rearrangement can be discontinuous. Zbl 0692.46028
Almgren, Frederick J. jun.; Lieb, Elliott H.
1989
Minimal surface forms. Zbl 0492.53003
Almgren, F. J. jun.
1982
Spherical symmetrization. Zbl 0656.49018
Almgren, F.
1987
Singularities of energy-minimizing maps from the ball to the sphere. Zbl 0663.58009
Almgren, Frederick J. jun.; Lieb, Elliott H.
1987
An introduction to regularity theory for parametric elliptic variational problems. Zbl 0268.49052
Allard, W. K.; Almgren, F. J. jun.
1973
The structure of limit varifolds associated with minimizing sequences of mappings. Zbl 0315.49018
Almgren, F. J. jun.
1974
Mass continuous cochains are differential forms. Zbl 0149.19003
Almgren, F. J. jun.
1965
An isoperimetric inequality. Zbl 0187.31203
Almgren, F. J. jun.
1964
Questions and answers about area-minimizing surfaces and geometric measure theory. Zbl 0812.49032
Almgren, Fred
1993
A maximum principle for elliptic variational problems. Zbl 0179.44102
Almgren, F. J. jun.
1969
Multiple valued functions in the geometric calculus of variations. Zbl 0575.49025
Almgren, F. J.; Super, B.
1984
Visualization of soap bubble geometries.
Leonardo 25, No. 3-4 (Spec. Issue).
Zbl 0803.51021
Almgren, Fred; Sullivan, John
1992
Basic techniques of geometric theory. Zbl 0635.53045
Almgren, F.
1988
The (non) continuity of symmetric decreasing rearrangement. Zbl 0704.46017
Almgren, Frederick J. jun.; Lieb, Elliott H.
1989
Existence and regularity of solutions to elliptic calculus of variations problems among surfaces of varying topological type and singularity structure. Zbl 0153.15903
Almgren, F. J. jun.
1967
Geometric measure theory and the calculus of variations. (Proceedings of the Summer Institute on Geometric Measure Theory and the Calculus of Variations Held at the Humboldt State University, Arcata, California, July 16 - August 3, 1984). Zbl 0577.00014
1986
Plateau’s problem. An invitation to varifold geometry. Revised ed. Zbl 0995.49001
Almgren, Frederick J. jun.
2001
Selected works of Frederick J. Almgren, Jr. Edited by Jean E. Taylor. Zbl 0966.01031
Almgren, Frederick J. jun.
1999
Homotopy with holes and minimal surfaces. Zbl 0731.53058
Almgren, Frederick; Browder, William
1991
Questions and answers about geometric evolution processes and crystal growth. Zbl 0869.60093
Almgren, Fred
1996
Minimal surfaces: Tangent cones, singularities, and topological types. Zbl 0433.49016
Almgren, F. J. jun.
1980
Plateau’s problem. An invitation to varifold geometry. Revised ed. Zbl 0995.49001
Almgren, Frederick J. jun.
2001
Almgren’s big regularity paper. $$Q$$-valued functions minimizing Dirichlet’s integral and the regularity of area-minimizing rectifiable currents up to codimension 2. Edited by V. Scheffer and Jean E. Taylor. Zbl 0985.49001
Almgren, Frederick J. jun.
2000
Mathematical existence of crystal growth with Gibbs-Thomson curvature effects. Zbl 0981.74041
Almgren, Fred; Wang, Lihe
2000
Selected works of Frederick J. Almgren, Jr. Edited by Jean E. Taylor. Zbl 0966.01031
Almgren, Frederick J. jun.
1999
The mean curvature integral is invariant under bending. Zbl 0914.53007
Almgren, Frederic J. jun.; Rivin, Igor
1998
Soap bubble clusters. Zbl 1017.49502
Almgren, Fred; Taylor, Jean E.
1996
Questions and answers about geometric evolution processes and crystal growth. Zbl 0869.60093
Almgren, Fred
1996
Flat flow is motion by crystalline curvature for curves with crystalline energies. Zbl 0867.58020
Almgren, Fred; Taylor, Jean E.
1995
Optimal geometry in equilibrium and growth. Zbl 0885.58015
Almgren, Fred; Taylor, Jean E.
1995
Curvature-driven flows: a variational approach. Zbl 0783.35002
Almgren, Fred; Taylor, Jean E.; Wang, Lihe
1993
Questions and answers about area-minimizing surfaces and geometric measure theory. Zbl 0812.49032
Almgren, Fred
1993
Visualization of soap bubble geometries.
Leonardo 25, No. 3-4 (Spec. Issue).
Zbl 0803.51021
Almgren, Fred; Sullivan, John
1992
Homotopy with holes and minimal surfaces. Zbl 0731.53058
Almgren, Frederick; Browder, William
1991
Symmetric decreasing rearrangement is sometimes continuous. Zbl 0688.46014
Almgren, Frederick J. jun.; Lieb, Elliott H.
1989
Symmetric decreasing rearrangement can be discontinuous. Zbl 0692.46028
Almgren, Frederick J. jun.; Lieb, Elliott H.
1989
The (non) continuity of symmetric decreasing rearrangement. Zbl 0704.46017
Almgren, Frederick J. jun.; Lieb, Elliott H.
1989
Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds. Zbl 0673.58013
Almgren, Frederick J. jun.; Lieb, Elliot H.
1988
Co-area, liquid crystals, and minimal surfaces. Zbl 0645.58015
Almgren, F.; Browder, W.; Lieb, E. H.
1988
Basic techniques of geometric theory. Zbl 0635.53045
Almgren, F.
1988
Spherical symmetrization. Zbl 0656.49018
Almgren, F.
1987
Singularities of energy-minimizing maps from the ball to the sphere. Zbl 0663.58009
Almgren, Frederick J. jun.; Lieb, Elliott H.
1987
Optimal isoperimetric inequalities. Zbl 0585.49030
Almgren, F.
1986
Deformations and multiple-valued functions. Zbl 0595.49028
Almgren, F.
1986
Geometric measure theory and the calculus of variations. (Proceedings of the Summer Institute on Geometric Measure Theory and the Calculus of Variations Held at the Humboldt State University, Arcata, California, July 16 - August 3, 1984). Zbl 0577.00014
1986
Optimal isoperimetric inequalities. Zbl 0572.49022
Almgren, F.
1985
Multiple valued functions in the geometric calculus of variations. Zbl 0575.49025
Almgren, F. J.; Super, B.
1984
Q valued functions minimizing Dirichlet’s integral and the regularity of area minimizing rectifiable currents up to codimension two. Zbl 0557.49021
Almgren, F. J. jun.
1983
Q valued functions minimizing Dirichlet’s integral and the regularity of area minimizing rectifiable currents up to codimension two. Zbl 0529.49021
Almgren, F. J. jun.
1983
Minimal surface forms. Zbl 0492.53003
Almgren, F. J. jun.
1982
On the radial behavior of minimal surfaces and the uniqueness of their tangent cones. Zbl 0437.53045
Allard, William K.; Almgren, Frederick J. jun.
1981
Minimal surfaces: Tangent cones, singularities, and topological types. Zbl 0433.49016
Almgren, F. J. jun.
1980
Existence of embedded solutions of Plateau’s problem. Zbl 0417.49051
Almgren, Frederick J. jun.; Simon, Leon
1979
Dirichlet’s problem for multiple valued functions and the regularity of mass minimizing integral currents. Zbl 0439.49028
Almgren, Frederick J. jun.
1979
Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals. Zbl 0386.49030
Schoen, Richard; Simon, Leon; Almgren, F. J.
1978
Examples of unknotted curves which bound only surfaces of high genus within their convex hulls. Zbl 0353.53001
Almgren, Frederick J. jun.; Thurston, William P.
1977
Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints. Zbl 0327.49043
Almgren, F. J. jun.
1976
The structure of stationary one dimensional varifolds with positive density. Zbl 0339.49020
Allard, W. K.; Almgren, F. J. jun.
1976
Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints. Zbl 0297.49041
Almgren, F. J. jun.
1975
The structure of limit varifolds associated with minimizing sequences of mappings. Zbl 0315.49018
Almgren, F. J. jun.
1974
An introduction to regularity theory for parametric elliptic variational problems. Zbl 0268.49052
Allard, W. K.; Almgren, F. J. jun.
1973
Measure theoretic geometry and elliptic variational problems. Zbl 0185.35202
Almgren, F. J. jun.
1969
A maximum principle for elliptic variational problems. Zbl 0179.44102
Almgren, F. J. jun.
1969
Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure. Zbl 0162.24703
Almgren, F. J. jun.
1968
Existence and regularity of solutions to elliptic calculus of variations problems among surfaces of varying topological type and singularity structure. Zbl 0153.15903
Almgren, F. J. jun.
1967
Some interior regularity theorems for minimal surfaces and an extension of Bernstein’s theorem. Zbl 0146.11905
Almgren, F. J. jun.
1966
Plateau’s problem. An invitation to varifold geometry. Zbl 0165.13201
Almgren, F. J. jun.
1966
Three theorems on manifolds with bounded mean curvature. Zbl 0131.19604
Almgren, F. J. jun.
1965
Mass continuous cochains are differential forms. Zbl 0149.19003
Almgren, F. J. jun.
1965
An isoperimetric inequality. Zbl 0187.31203
Almgren, F. J. jun.
1964
The homotopy groups of the integral cycle groups. Zbl 0118.18503
Almgren, F. J. jun.
1962
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### Cited by 974 Authors

 23 Morgan, Frank 22 Novaga, Matteo 15 Almgren, Frederick Justin jun. 15 Chambolle, Antonin 15 De Lellis, Camillo 14 Felli, Veronica 12 Lin, Fang Hua 11 De Philippis, Guido 11 Fusco, Nicola 11 Hardt, Robert M. 11 Morini, Massimiliano 9 Bellettini, Giovanni 9 Duzaar, Frank 9 Maggi, Francesco 9 Marques, Fernando Codá 8 Arroja Neves, André 8 Braides, Andrea 8 Harrison, Jenny C. 8 Minicozzi, William Philip II 8 Spadaro, Emanuele Nunzio 7 Colding, Tobias Holck 7 Gromov, Mikhael Leonidovich 7 Simon, Leon Melvin 7 Tonegawa, Yoshihiro 7 White, Brian Cabell 6 Ambrosio, Luigi 6 Esedoglu, Selim 6 Gazzola, Filippo 6 Giaquinta, Mariano 6 Giga, Yoshikazu 6 Laux, Tim 6 Lawson, Herbert Blaine jun. 6 Leonardi, Gian Paolo 6 Liang, Xiangyu 6 Lieb, Elliott Hershel 6 Millot, Vincent 6 Ponsiglione, Marcello 6 Rakotoson, Jean-Michel 6 Wei, Juncheng 6 Wickramasekera, Neshan 6 Zhou, Xin 5 Brendle, Simon 5 Caraballo, David G. 5 Caselles Costa, Vicent 5 Ferrero, Alberto 5 Figalli, Alessio 5 Goblet, Jordan 5 Hadzic, Mahir 5 Hsiang, Wu-Yi 5 Jost, Jürgen 5 Pisante, Adriano 5 Pugh, Harrison 5 Rivière, Tristan 5 Rosales, Leobardo 5 Spolaor, Luca 5 Taylor, Jean Ellen 5 Terracini, Susanna 5 Valtorta, Daniele 4 Abatangelo, Laura 4 Allard, William K. 4 Brézis, Haïm 4 Charon, Nicolas 4 Cianchi, Andrea 4 Cicalese, Marco 4 De Pauw, Thierry 4 De Rosa, Antonio 4 Fonseca, Irene 4 Ghiraldin, Francesco 4 Górka, Przemysław 4 Grüter, Michael 4 Hildebrandt, Stefan 4 Hirsch, Jonas 4 Hong, Minchun 4 Kholmatov, Shokhrukh Yusufovich 4 Menne, Ulrich 4 Mironescu, Petru 4 Modica, Giuseppe 4 Mucci, Domenico 4 Naber, Aaron C. 4 Noris, Benedetta 4 Ok, Jihoon 4 Otto, Felix 4 Parks, Harold R. 4 Petrosyan, Arshak 4 Ritoré, Manuel 4 Röger, Matthias 4 Schoen, Richard Melvin 4 Scilla, Giovanni 4 Seo, Keomkyo 4 Soucek, Jiri 4 Torres Ledesma, César Enrique 4 Van Gennip, Yves 4 Wadade, Hidemitsu 3 Agudelo, Oscar Mauricio 3 Bögelein, Verena 3 Bombieri, Enrico 3 Brakke, Kenneth A. 3 Brasco, Lorenzo 3 Caffarelli, Luis Ángel 3 Carlen, Eric Anders ...and 874 more Authors
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### Cited in 203 Serials

 81 Calculus of Variations and Partial Differential Equations 50 The Journal of Geometric Analysis 45 Archive for Rational Mechanics and Analysis 30 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 27 Proceedings of the American Mathematical Society 25 Transactions of the American Mathematical Society 23 Inventiones Mathematicae 23 Journal of Functional Analysis 19 Journal of Differential Equations 18 Advances in Mathematics 17 Mathematische Annalen 16 Manuscripta Mathematica 16 Bulletin of the American Mathematical Society. New Series 14 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 14 Journal de Mathématiques Pures et Appliquées. Neuvième Série 13 Journal für die Reine und Angewandte Mathematik 12 Duke Mathematical Journal 11 Communications in Mathematical Physics 11 Communications in Partial Differential Equations 11 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 11 Annals of Mathematics. Second Series 11 Bulletin of the American Mathematical Society 10 Communications on Pure and Applied Mathematics 10 Acta Mathematica 10 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 10 Journal of the European Mathematical Society (JEMS) 9 Mathematische Zeitschrift 9 Communications on Pure and Applied Analysis 9 Advances in Calculus of Variations 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Geometric and Functional Analysis. GAFA 8 SIAM Journal on Mathematical Analysis 7 Journal of Mathematical Analysis and Applications 7 Geometriae Dedicata 7 Rendiconti del Seminario Matematico della Università di Padova 7 Annals of Global Analysis and Geometry 7 Revista Matemática Iberoamericana 7 Discrete and Continuous Dynamical Systems 6 Journal of Computational Physics 6 Annales de l’Institut Fourier 6 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 6 Journal of the American Mathematical Society 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Journal of Scientific Computing 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 4 Journal d’Analyse Mathématique 4 Journal of Geometry and Physics 4 Publications Mathématiques 4 Journal of Differential Geometry 4 Journal of Soviet Mathematics 4 Differential Geometry and its Applications 4 NoDEA. Nonlinear Differential Equations and Applications 4 Communications in Contemporary Mathematics 4 Milan Journal of Mathematics 4 Discrete and Continuous Dynamical Systems. Series S 4 Bulletin of Mathematical Sciences 4 Nonlinear Analysis. Theory, Methods & Applications 3 Applicable Analysis 3 Archiv der Mathematik 3 Tôhoku Mathematical Journal. Second Series 3 Physica D 3 Applied Mathematics Letters 3 Japan Journal of Industrial and Applied Mathematics 3 Journal of Nonlinear Science 3 Potential Analysis 3 Journal of Mathematical Sciences (New York) 3 Electronic Research Announcements of the American Mathematical Society 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Journal of Fixed Point Theory and Applications 3 Networks and Heterogeneous Media 3 Analysis & PDE 3 Journal of Topology and Analysis 3 Science China. Mathematics 3 Advances in Nonlinear Analysis 3 Annals of PDE 2 Computers & Mathematics with Applications 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Mathematical Physics 2 Journal of Statistical Physics 2 Mathematical Methods in the Applied Sciences 2 The Mathematical Intelligencer 2 American Journal of Mathematics 2 Applied Mathematics and Optimization 2 Compositio Mathematica 2 Indiana University Mathematics Journal 2 Memoirs of the American Mathematical Society 2 Rendiconti del Seminario Matemàtico e Fisico di Milano 2 Topology and its Applications 2 Zeitschrift für Analysis und ihre Anwendungen 2 Acta Mathematicae Applicatae Sinica. English Series 2 Probability Theory and Related Fields 2 Discrete & Computational Geometry 2 Publicacions Matemàtiques 2 European Journal of Applied Mathematics 2 Applications of Mathematics 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Topological Methods in Nonlinear Analysis 2 St. Petersburg Mathematical Journal 2 International Journal of Computer Vision ...and 103 more Serials
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### Cited in 50 Fields

 424 Calculus of variations and optimal control; optimization (49-XX) 373 Differential geometry (53-XX) 331 Partial differential equations (35-XX) 151 Global analysis, analysis on manifolds (58-XX) 65 Functional analysis (46-XX) 63 Measure and integration (28-XX) 55 Real functions (26-XX) 51 Mechanics of deformable solids (74-XX) 39 Fluid mechanics (76-XX) 39 Statistical mechanics, structure of matter (82-XX) 38 Numerical analysis (65-XX) 28 Convex and discrete geometry (52-XX) 23 Operator theory (47-XX) 22 Manifolds and cell complexes (57-XX) 17 Classical thermodynamics, heat transfer (80-XX) 14 Probability theory and stochastic processes (60-XX) 12 Computer science (68-XX) 11 Algebraic geometry (14-XX) 11 Several complex variables and analytic spaces (32-XX) 11 Ordinary differential equations (34-XX) 10 Potential theory (31-XX) 10 Geometry (51-XX) 10 Algebraic topology (55-XX) 9 Quantum theory (81-XX) 8 Functions of a complex variable (30-XX) 7 General topology (54-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Relativity and gravitational theory (83-XX) 5 History and biography (01-XX) 5 Topological groups, Lie groups (22-XX) 5 Integral equations (45-XX) 5 Information and communication theory, circuits (94-XX) 4 Group theory and generalizations (20-XX) 4 Operations research, mathematical programming (90-XX) 3 Combinatorics (05-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Statistics (62-XX) 3 Biology and other natural sciences (92-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Abstract harmonic analysis (43-XX) 2 Mechanics of particles and systems (70-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Commutative algebra (13-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Optics, electromagnetic theory (78-XX)

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