## Perel’man, Grigoriĭ Yakovlevich

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 Author ID: perelman.grigori-yakovlevich Published as: Perel’man, G. Ya.; Perelman, Grisha; Perelman, G.; Perel’man, G. more...less Further Spellings: Перельман Григорий Яковлевич External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · GND · IdRef Awards: EMS Prize (1996) · Fields Medal (2006)
 Documents Indexed: 22 Publications since 1985 Biographic References: 7 Publications Co-Authors: 4 Co-Authors with 3 Joint Publications 146 Co-Co-Authors

### Co-Authors

 19 single-authored 1 Burago, Yuriĭ Dmitrievich 1 Gromov, Mikhael Leonidovich 1 Petrunin, Anton Mikhailovich 1 Polikanova, Irina Viktorovna
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### Serials

 3 arXiv e-print service 2 Journal of Soviet Mathematics 2 Sibirskiĭ Matematicheskiĭ Zhurnal 2 Ukrainskiĭ Geometricheskiĭ Sbornik 2 St. Petersburg Mathematical Journal 1 Russian Mathematical Surveys 1 Journal of Differential Geometry 1 Mathematische Zeitschrift 1 Siberian Mathematical Journal 1 Journal of the American Mathematical Society 1 Geometric and Functional Analysis. GAFA

### Fields

 18 Differential geometry (53-XX) 4 Convex and discrete geometry (52-XX) 4 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX)

### Citations contained in zbMATH Open

19 Publications have been cited 1,672 times in 1,132 Documents Cited by Year
The entropy formula for the Ricci flow and its geometric applications. Zbl 1130.53001
Perelman, Grisha
2002
Ricci flow with surgery on three-manifolds. Zbl 1130.53002
Perelman, Grisha
2003
Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. Zbl 1130.53003
Perelman, Grisha
2003
A. D. Alexandrov spaces with curvature bounded below. Zbl 0802.53018
Burago, Yu.; Gromov, M.; Perel’man, G.
1992
Proof of the soul conjecture of Cheeger and Gromoll. Zbl 0818.53056
Perelman, Grisha
1994
Manifolds of positive Ricci curvature with almost maximal volume. Zbl 0799.53050
Perelman, Grisha
1994
Spaces with curvature bounded below. Zbl 0838.53033
Perelman, Grisha
1995
Construction of manifolds of positive Ricci curvature with big volume and large Betti numbers. Zbl 0890.53038
Perelman, G.
1997
Extremal subsets in Aleksandrov spaces and the generalized Liberman theorem. Zbl 0802.53019
Perel’man, G. Ya.; Petrunin, A. M.
1993
A complete Riemannian manifold of positive Ricci curvature with Euclidean volume growth and nonunique asymptotic cone. Zbl 0887.53038
Perelman, G.
1997
Elements of Morse theory on Aleksandrov spaces. Zbl 0815.53072
Perel’man, G. Ya.
1993
A diameter sphere theorem for manifolds of positive Ricci curvature. Zbl 0831.53033
Perelman, Grisha
1995
Collapsing with no proper extremal subsets. Zbl 0887.53049
Perelman, Grisha
1997
On the k-radii of a convex body. Zbl 0623.52007
Perel’man, G. Ya.
1987
Widths of nonnegatively curved spaces. Zbl 0845.53031
Perelman, Grisha
1995
On the k radii of a convex body. Zbl 0637.52009
Perel’man, G. Ya.
1987
Example of a complete saddle surface in $$R^ 4$$ with Gaussian curvature bounded away from zero. Zbl 0741.53037
Perel’man, G. Ya.
1989
An example of a complete saddle surface in $$R^ 4$$ with Gaussian curvature different from zero. Zbl 0714.53035
Perel’man, G. Ya.
1989
A remark on the Helly theorem. Zbl 0615.52009
Polikanova, I. V.; Perel’man, G. Ya.
1986
Ricci flow with surgery on three-manifolds. Zbl 1130.53002
Perelman, Grisha
2003
Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. Zbl 1130.53003
Perelman, Grisha
2003
The entropy formula for the Ricci flow and its geometric applications. Zbl 1130.53001
Perelman, Grisha
2002
Construction of manifolds of positive Ricci curvature with big volume and large Betti numbers. Zbl 0890.53038
Perelman, G.
1997
A complete Riemannian manifold of positive Ricci curvature with Euclidean volume growth and nonunique asymptotic cone. Zbl 0887.53038
Perelman, G.
1997
Collapsing with no proper extremal subsets. Zbl 0887.53049
Perelman, Grisha
1997
Spaces with curvature bounded below. Zbl 0838.53033
Perelman, Grisha
1995
A diameter sphere theorem for manifolds of positive Ricci curvature. Zbl 0831.53033
Perelman, Grisha
1995
Widths of nonnegatively curved spaces. Zbl 0845.53031
Perelman, Grisha
1995
Proof of the soul conjecture of Cheeger and Gromoll. Zbl 0818.53056
Perelman, Grisha
1994
Manifolds of positive Ricci curvature with almost maximal volume. Zbl 0799.53050
Perelman, Grisha
1994
Extremal subsets in Aleksandrov spaces and the generalized Liberman theorem. Zbl 0802.53019
Perel&rsquo;man, G. Ya.; Petrunin, A. M.
1993
Elements of Morse theory on Aleksandrov spaces. Zbl 0815.53072
Perel&rsquo;man, G. Ya.
1993
A. D. Alexandrov spaces with curvature bounded below. Zbl 0802.53018
Burago, Yu.; Gromov, M.; Perel&rsquo;man, G.
1992
Example of a complete saddle surface in $$R^ 4$$ with Gaussian curvature bounded away from zero. Zbl 0741.53037
Perel&rsquo;man, G. Ya.
1989
An example of a complete saddle surface in $$R^ 4$$ with Gaussian curvature different from zero. Zbl 0714.53035
Perel&rsquo;man, G. Ya.
1989
On the k-radii of a convex body. Zbl 0623.52007
Perel&rsquo;man, G. Ya.
1987
On the k radii of a convex body. Zbl 0637.52009
Perel&rsquo;man, G. Ya.
1987
A remark on the Helly theorem. Zbl 0615.52009
Polikanova, I. V.; Perel&rsquo;man, G. Ya.
1986
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### Cited by 1,028 Authors

 24 Wu, Jiayong 20 Ma, Li 15 Wang, Linfeng 14 Abolarinwa, Abimbola 14 Azami, Shahroud 14 Brendle, Simon 14 Cao, Huai-Dong 13 Guo, Hongxin 13 Lu, Peng 13 Tian, Gang 12 Chow, Bennett 12 Lott, John 12 Zhang, Qi-Shuhuason 11 Catino, Giovanni 10 Cao, Xiaodong 10 Streets, Jeffrey D. 10 Wang, Bing 10 Zhang, Yongjia 9 Chen, Xiuxiong 9 Galaz-Garcia, Fernando 9 Li, Xiang-Dong 9 Vacaru, Sergiu Ion 9 Zhang, Zhenlei 9 Zhu, Anqiang 9 Zhu, Xiaohua 8 Bamler, Richard H. 8 Cheng, Liang 8 Fang, Shouwen 8 Haslhofer, Robert 8 Rong, Xiaochun 8 Searle, Catherine 7 Carfora, Mauro 7 Colding, Tobias Holck 7 Fang, Fuquan 7 Guijarro, Luis 7 Honda, Shouhei 7 Ni, Lei 7 Sesum, Natasa 7 Suh, Young Jin 7 Ye, Rugang 7 Zheng, Yu 7 Zhu, Meng 6 Chaubey, Sudhakar Kumar 6 Chen, Chih-Wei 6 De, Uday Chand 6 Deng, Yuxing 6 Hsu, Shu-Yu 6 Kapovitch, Vitali 6 Lackenby, Marc 6 Lee, Man-Chun 6 Mastrolia, Paolo 6 Munteanu, Ovidiu 6 Philipowski, Robert 6 Topping, Peter Miles 6 Wei, Guofang 6 Wylie, William C. 6 Yu, Chengjie 6 Zhang, Liangdi 5 Besson, Gérard 5 Cho, Jong Taek 5 Ghosh, Amalendu 5 Hall, Stuart James 5 Harvey, John Matthew 5 Hou, Songbo 5 Huang, Shaosai 5 Hui, Shyamal Kumar 5 Mantegazza, Carlo 5 Munn, Michael 5 Petersen, Peter V 5 Sarkar, Avijit 5 Sinestrari, Carlo 5 Song, Jian 5 Tam, Luen-Fai 5 Yamaguchi, Takao 5 Zhang, Yuguang 4 Agol, Ian 4 Barbosa, Ezequiel R. 4 Cabezas-Rivas, Esther 4 Chen, Qiang 4 Hua, Bobo 4 Huisken, Gerhard 4 Ishida, Masashi 4 Kimura, Makoto 4 Kleiner, Bruce 4 Lüst, Dieter 4 Lytchak, Alexander 4 Ma, Zilu 4 Maillot, Sylvain 4 Minicozzi, William Philip II 4 Naber, Aaron C. 4 Ribeiro, Ernani jun. 4 Sharma, Ramesh 4 Shioya, Takashi 4 Thalmaier, Anton 4 Walschap, Gerard 4 Wang, Changliang 4 Wang, Jiaping 4 Wang, Yusheng 4 Wraith, David J. 4 Wu, Guoqiang ...and 928 more Authors
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### Cited in 229 Serials

 72 The Journal of Geometric Analysis 54 Proceedings of the American Mathematical Society 37 Annals of Global Analysis and Geometry 35 Calculus of Variations and Partial Differential Equations 33 Advances in Mathematics 32 Geometriae Dedicata 31 Transactions of the American Mathematical Society 30 Journal of Geometry and Physics 30 Mathematische Annalen 24 Geometry & Topology 22 Inventiones Mathematicae 21 Journal of Functional Analysis 20 Differential Geometry and its Applications 19 Duke Mathematical Journal 17 Journal für die Reine und Angewandte Mathematik 17 Mathematische Zeitschrift 17 Science China. Mathematics 13 Communications in Mathematical Physics 13 Journal of Mathematical Analysis and Applications 12 Comptes Rendus. Mathématique. Académie des Sciences, Paris 11 Manuscripta Mathematica 11 Geometric and Functional Analysis. GAFA 11 Algebraic & Geometric Topology 10 Results in Mathematics 10 Journal of the American Mathematical Society 10 Journal of the European Mathematical Society (JEMS) 9 Nuclear Physics. B 9 Acta Mathematica Sinica. English Series 9 Journal of High Energy Physics 9 Advances in Geometry 8 Archiv der Mathematik 8 Monatshefte für Mathematik 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Tôhoku Mathematical Journal. Second Series 8 International Journal of Mathematics 8 Annals of Mathematics. Second Series 8 Frontiers of Mathematics in China 7 Communications on Pure and Applied Mathematics 7 Chinese Annals of Mathematics. Series B 7 Bulletin of the American Mathematical Society. New Series 7 Mediterranean Journal of Mathematics 6 Journal of Mathematical Physics 6 Journal of the Korean Mathematical Society 6 Topology and its Applications 6 Discrete & Computational Geometry 6 Annals of Physics 6 Communications of the Korean Mathematical Society 6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 6 Communications in Mathematics and Statistics 5 Letters in Mathematical Physics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Bulletin of the Brazilian Mathematical Society. New Series 4 General Relativity and Gravitation 4 Annales de l’Institut Fourier 4 Journal of Differential Equations 4 Journal of Geometry 4 Journal of the Mathematical Society of Japan 4 Osaka Journal of Mathematics 4 Bulletin of the Iranian Mathematical Society 4 Russian Mathematics 4 Potential Analysis 4 Bulletin des Sciences Mathématiques 4 Communications in Contemporary Mathematics 4 Acta Mathematica Scientia. Series B. (English Edition) 3 Archive for Rational Mechanics and Analysis 3 Classical and Quantum Gravity 3 Israel Journal of Mathematics 3 Mathematical Notes 3 Beiträge zur Algebra und Geometrie 3 Acta Mathematica 3 Bulletin of the London Mathematical Society 3 Proceedings of the Japan Academy. Series A 3 Revista Matemática Iberoamericana 3 Facta Universitatis. Series Mathematics and Informatics 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Journal of Mathematical Sciences (New York) 3 St. Petersburg Mathematical Journal 3 Conformal Geometry and Dynamics 3 Journal of Inequalities and Applications 3 Journal of Evolution Equations 3 Journal of Topology 3 Japanese Journal of Mathematics. 3rd Series 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 Bulletin of Mathematical Sciences 3 Afrika Matematika 3 Analysis and Geometry in Metric Spaces 3 Korean Journal of Mathematics 2 Indian Journal of Pure & Applied Mathematics 2 International Journal of Theoretical Physics 2 Mathematical Methods in the Applied Sciences 2 Reports on Mathematical Physics 2 Rocky Mountain Journal of Mathematics 2 Ukrainian Mathematical Journal 2 Chaos, Solitons and Fractals 2 The Mathematical Intelligencer 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Canadian Mathematical Bulletin 2 Journal of Differential Geometry 2 Journal of Pure and Applied Algebra ...and 129 more Serials
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### Cited in 53 Fields

 916 Differential geometry (53-XX) 234 Global analysis, analysis on manifolds (58-XX) 182 Partial differential equations (35-XX) 172 Manifolds and cell complexes (57-XX) 59 Relativity and gravitational theory (83-XX) 49 Several complex variables and analytic spaces (32-XX) 32 Quantum theory (81-XX) 27 Group theory and generalizations (20-XX) 26 Dynamical systems and ergodic theory (37-XX) 25 Calculus of variations and optimal control; optimization (49-XX) 24 Probability theory and stochastic processes (60-XX) 23 Convex and discrete geometry (52-XX) 21 Algebraic geometry (14-XX) 16 Geometry (51-XX) 15 Combinatorics (05-XX) 11 Functional analysis (46-XX) 10 Functions of a complex variable (30-XX) 10 General topology (54-XX) 9 Algebraic topology (55-XX) 9 Computer science (68-XX) 8 Topological groups, Lie groups (22-XX) 7 Real functions (26-XX) 7 Potential theory (31-XX) 6 Operator theory (47-XX) 6 Mechanics of particles and systems (70-XX) 5 General and overarching topics; collections (00-XX) 5 History and biography (01-XX) 5 Measure and integration (28-XX) 5 Numerical analysis (65-XX) 4 Mechanics of deformable solids (74-XX) 4 Fluid mechanics (76-XX) 3 Number theory (11-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Operations research, mathematical programming (90-XX) 2 Associative rings and algebras (16-XX) 2 Nonassociative rings and algebras (17-XX) 2 Category theory; homological algebra (18-XX) 2 $$K$$-theory (19-XX) 2 Ordinary differential equations (34-XX) 2 Approximations and expansions (41-XX) 2 Statistics (62-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX)

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