# zbMATH — the first resource for mathematics

## Hamilton, Richard S.

Compute Distance To:
 Author ID: hamilton.richard-s Published as: Hamilton, R.; Hamilton, R. S.; Hamilton, Richard; Hamilton, Richard S. Homepage: https://www.math.columbia.edu/people/directory/name/richard-hamilton/ External Links: MGP · Wikidata · GND Awards: Clay Research Award (2003) · Shaw Prize (2011)
 Documents Indexed: 48 Publications since 1969, including 2 Books Biographic References: 1 Publication
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#### Co-Authors

 28 single-authored 9 Daskalopoulos, Panagiota 3 Sesum, Natasa 2 Chow, Bennett 1 Cao, Huai-Dong 1 Cao, Xiaodong 1 Chern, Shiing-Shen 1 Earle, Clifford J. 1 Gage, M. 1 Grayson, Matthew A. 1 Isenberg, James A. 1 Lee, Ki-Ahm 1 Yau, Shing-Tung
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#### Serials

 13 Journal of Differential Geometry 11 Communications in Analysis and Geometry 2 American Journal of Mathematics 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Journal für die Reine und Angewandte Mathematik 1 Transactions of the American Mathematical Society 1 Journal of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 Bulletin of the American Mathematical Society. New Series 1 Turkish Journal of Mathematics 1 Mathematical Research Letters 1 The Asian Journal of Mathematics 1 Lecture Notes in Mathematics
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#### Fields

 35 Differential geometry (53-XX) 19 Global analysis, analysis on manifolds (58-XX) 16 Partial differential equations (35-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Manifolds and cell complexes (57-XX) 2 Functions of a complex variable (30-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Convex and discrete geometry (52-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX)

#### Citations contained in zbMATH

46 Publications have been cited 3,105 times in 2,234 Documents Cited by Year
Three-manifolds with positive Ricci curvature. Zbl 0504.53034
Hamilton, Richard S.
1982
The inverse function theorem of Nash and Moser. Zbl 0499.58003
Hamilton, Richard S.
1982
The heat equation shrinking convex plane curves. Zbl 0621.53001
Gage, M.; Hamilton, R. S.
1986
The formation of singularities in the Ricci flow. Zbl 0867.53030
Hamilton, Richard S.
1995
Four-manifolds with positive curvature operator. Zbl 0628.53042
Hamilton, Richard S.
1986
Harmonic maps of manifolds with boundary. Zbl 0308.35003
Hamilton, Richard S.
1975
A matrix Harnack estimate for the heat equation. Zbl 0799.53048
Hamilton, Richard S.
1993
The Harnack estimate for the Ricci flow. Zbl 0804.53023
Hamilton, Richard S.
1993
A compactness property for solutions of the Ricci flow. Zbl 0840.53029
Hamilton, Richard S.
1995
The Ricci flow on surfaces. Zbl 0663.53031
Hamilton, Richard S.
1988
Harnack estimate for the mean curvature flow. Zbl 0827.53006
Hamilton, Richard S.
1995
Regularity of the free boundary for the porous medium equation. Zbl 0910.35145
1998
Extremal quasiconformal mappings with prescribed boundary values. Zbl 0209.11102
Hamilton, R. S.
1969
Four-manifolds with positive isotropic curvature. Zbl 0892.53018
Hamilton, Richard S.
1997
A fixed point theorem for holomorphic mappings. Zbl 0205.14702
Earle, C. J.; Hamilton, R. S.
1970
Differential Harnack estimates for time-dependent heat equations with potentials. Zbl 1183.53059
Cao, Xiaodong; Hamilton, Richard S.
2009
Non-singular solutions of the Ricci flow on three-manifolds. Zbl 0939.53024
Hamilton, Richard S.
1999
Constrained and linear Harnack inequalities for parabolic equations. Zbl 0903.58054
Chow, Bennett; Hamilton, Richard S.
1997
On Riemannian metrics adapted to three-dimensional contact manifolds. Zbl 0561.53039
Chern, S. S.; Hamilton, R. S.
1985
Monotonicity formulas for parabolic flows on manifolds. Zbl 0779.58037
Hamilton, Richard S.
1993
Eternal solutions to the Ricci flow. Zbl 0792.53041
Hamilton, Richard S.
1993
Classification of ancient compact solutions to the Ricci flow on surfaces. Zbl 1257.53095
Daskalopoulos, Panagiota; Hamilton, Richard; Sesum, Natasa
2012
Classification of compact ancient solutions to the curve shortening flow. Zbl 1205.53070
Daskalopoulos, Panagiota; Hamilton, Richard; Sesum, Natasa
2010
Deformation of complex structures on manifolds with boundary. I: The stable case. Zbl 0394.32010
Hamilton, Richard S.
1977
The free boundary in the Gauss curvature flow with flat sides. Zbl 0931.53031
1999
Convex hypersurfaces with pinched second fundamental form. Zbl 0843.53002
Hamilton, Richard S.
1994
Isoperimetric estimates for the curve shrinking flow in the plane. Zbl 0846.51010
Hamilton, Richard S.
1995
Geometric estimates for the logarithmic fast diffusion equation. Zbl 1070.53041
2004
The cross curvature flow of 3-manifolds with negative sectional curvature. Zbl 1064.53045
Chow, Bennett; Hamilton, Richard S.
2004
All time $$C^\infty$$-regularity of the interface in degenerate diffusion: A geometric approach. Zbl 1017.35052
Daskalopoulos, P.; Hamilton, R.; Lee, K.
2001
Li-Yau estimates and their Harnack inequalities. Zbl 1263.58007
Hamilton, Richard S.
2011
The formation of singularities in the harmonic map heat flow. Zbl 0872.58021
Grayson, Matthew; Hamilton, Richard S.
1996
Gradient Kähler-Ricci solitons and periodic orbits. Zbl 1027.53074
Cao, Huai-Dong; Hamilton, Richard S.
2000
An isoperimetric estimate for the Ricci flow on the two-sphere. Zbl 0852.58027
Hamilton, Richard S.
1995
Quasi-convergence of Ricci flow for a class of metrics. Zbl 0841.53058
Hamilton, Richard; Isenberg, James
1993
Deformation of complex structures on manifolds with boundary. II: Families of non-coercive boundary value problems. Zbl 0512.32015
Hamilton, Richard S.
1979
The free boundary for the $$N$$-dimensional porous medium equation. Zbl 0886.35114
1997
$$C^{\infty}$$-regularity of the interface of the evolution $$p$$-Laplacian equation. Zbl 0929.35071
1998
Worn stones with flat sides. Zbl 0882.52002
Hamilton, Richard S.
1994
Deformation of complex structures on manifolds with boundary. II: Families of non-coercive boundary value problems. Zbl 0474.58020
Hamilton, Richard S.
1979
The Harnack estimate for the Ricci flow on a surface – revisited. Zbl 0894.53041
Hamilton, Richard S.; Yau, Shing-Tung
1997
Remarks on the entropy and Harnack estimates for the Gauss curvature flow. Zbl 0839.53050
Hamilton, Richard S.
1994
The Ricci curvature equation. Zbl 0557.53018
Hamilton, Richard
1984
Properties of the solutions of the conjugate heat equations. Zbl 1160.53019
Hamilton, Richard; Sesum, Natasa
2009
Non-hyperelliptic Riemann surfaces. Zbl 0207.07901
Hamilton, R. S.
1969
Harmonic mean curvature flow on surfaces of negative Gaussian curvature. Zbl 1127.53058
2006
Classification of ancient compact solutions to the Ricci flow on surfaces. Zbl 1257.53095
Daskalopoulos, Panagiota; Hamilton, Richard; Sesum, Natasa
2012
Li-Yau estimates and their Harnack inequalities. Zbl 1263.58007
Hamilton, Richard S.
2011
Classification of compact ancient solutions to the curve shortening flow. Zbl 1205.53070
Daskalopoulos, Panagiota; Hamilton, Richard; Sesum, Natasa
2010
Differential Harnack estimates for time-dependent heat equations with potentials. Zbl 1183.53059
Cao, Xiaodong; Hamilton, Richard S.
2009
Properties of the solutions of the conjugate heat equations. Zbl 1160.53019
Hamilton, Richard; Sesum, Natasa
2009
Harmonic mean curvature flow on surfaces of negative Gaussian curvature. Zbl 1127.53058
2006
Geometric estimates for the logarithmic fast diffusion equation. Zbl 1070.53041
2004
The cross curvature flow of 3-manifolds with negative sectional curvature. Zbl 1064.53045
Chow, Bennett; Hamilton, Richard S.
2004
All time $$C^\infty$$-regularity of the interface in degenerate diffusion: A geometric approach. Zbl 1017.35052
Daskalopoulos, P.; Hamilton, R.; Lee, K.
2001
Gradient Kähler-Ricci solitons and periodic orbits. Zbl 1027.53074
Cao, Huai-Dong; Hamilton, Richard S.
2000
Non-singular solutions of the Ricci flow on three-manifolds. Zbl 0939.53024
Hamilton, Richard S.
1999
The free boundary in the Gauss curvature flow with flat sides. Zbl 0931.53031
1999
Regularity of the free boundary for the porous medium equation. Zbl 0910.35145
1998
$$C^{\infty}$$-regularity of the interface of the evolution $$p$$-Laplacian equation. Zbl 0929.35071
1998
Four-manifolds with positive isotropic curvature. Zbl 0892.53018
Hamilton, Richard S.
1997
Constrained and linear Harnack inequalities for parabolic equations. Zbl 0903.58054
Chow, Bennett; Hamilton, Richard S.
1997
The free boundary for the $$N$$-dimensional porous medium equation. Zbl 0886.35114
1997
The Harnack estimate for the Ricci flow on a surface – revisited. Zbl 0894.53041
Hamilton, Richard S.; Yau, Shing-Tung
1997
The formation of singularities in the harmonic map heat flow. Zbl 0872.58021
Grayson, Matthew; Hamilton, Richard S.
1996
The formation of singularities in the Ricci flow. Zbl 0867.53030
Hamilton, Richard S.
1995
A compactness property for solutions of the Ricci flow. Zbl 0840.53029
Hamilton, Richard S.
1995
Harnack estimate for the mean curvature flow. Zbl 0827.53006
Hamilton, Richard S.
1995
Isoperimetric estimates for the curve shrinking flow in the plane. Zbl 0846.51010
Hamilton, Richard S.
1995
An isoperimetric estimate for the Ricci flow on the two-sphere. Zbl 0852.58027
Hamilton, Richard S.
1995
Convex hypersurfaces with pinched second fundamental form. Zbl 0843.53002
Hamilton, Richard S.
1994
Worn stones with flat sides. Zbl 0882.52002
Hamilton, Richard S.
1994
Remarks on the entropy and Harnack estimates for the Gauss curvature flow. Zbl 0839.53050
Hamilton, Richard S.
1994
A matrix Harnack estimate for the heat equation. Zbl 0799.53048
Hamilton, Richard S.
1993
The Harnack estimate for the Ricci flow. Zbl 0804.53023
Hamilton, Richard S.
1993
Monotonicity formulas for parabolic flows on manifolds. Zbl 0779.58037
Hamilton, Richard S.
1993
Eternal solutions to the Ricci flow. Zbl 0792.53041
Hamilton, Richard S.
1993
Quasi-convergence of Ricci flow for a class of metrics. Zbl 0841.53058
Hamilton, Richard; Isenberg, James
1993
The Ricci flow on surfaces. Zbl 0663.53031
Hamilton, Richard S.
1988
The heat equation shrinking convex plane curves. Zbl 0621.53001
Gage, M.; Hamilton, R. S.
1986
Four-manifolds with positive curvature operator. Zbl 0628.53042
Hamilton, Richard S.
1986
On Riemannian metrics adapted to three-dimensional contact manifolds. Zbl 0561.53039
Chern, S. S.; Hamilton, R. S.
1985
The Ricci curvature equation. Zbl 0557.53018
Hamilton, Richard
1984
Three-manifolds with positive Ricci curvature. Zbl 0504.53034
Hamilton, Richard S.
1982
The inverse function theorem of Nash and Moser. Zbl 0499.58003
Hamilton, Richard S.
1982
Deformation of complex structures on manifolds with boundary. II: Families of non-coercive boundary value problems. Zbl 0512.32015
Hamilton, Richard S.
1979
Deformation of complex structures on manifolds with boundary. II: Families of non-coercive boundary value problems. Zbl 0474.58020
Hamilton, Richard S.
1979
Deformation of complex structures on manifolds with boundary. I: The stable case. Zbl 0394.32010
Hamilton, Richard S.
1977
Harmonic maps of manifolds with boundary. Zbl 0308.35003
Hamilton, Richard S.
1975
A fixed point theorem for holomorphic mappings. Zbl 0205.14702
Earle, C. J.; Hamilton, R. S.
1970
Extremal quasiconformal mappings with prescribed boundary values. Zbl 0209.11102
Hamilton, R. S.
1969
Non-hyperelliptic Riemann surfaces. Zbl 0207.07901
Hamilton, R. S.
1969
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#### Cited by 2,081 Authors

 28 Ma, Li 22 Wu, Jiayong 20 Brendle, Simon 18 Tsai, Dong-Ho 17 Daskalopoulos, Panagiota 16 Cao, Huai-Dong 15 Cao, Xiaodong 15 Chow, Bennett 14 Chen, Xiuxiong 14 Lee, Ki-Ahm 14 Sesum, Natasa 14 Tian, Gang 13 Neeb, Karl-Hermann 13 Streets, Jeffrey D. 12 Ni, Lei 12 Poppenberg, Markus 12 Zhu, Anqiang 12 Zhu, Xiaohua 11 Feehan, Paul M. N. 11 Haslhofer, Robert 11 Mantegazza, Carlo 11 Novaga, Matteo 11 Wheeler, Glen E. 10 Catino, Giovanni 10 Cheng, Liang 10 Kolev, Boris 10 Pan, Shengliang 10 Perrone, Domenico 10 Reich, Simeon 10 Wang, Xiaoliu 9 Andrews, Ben 9 Angenent, Sigurd Bernardus 9 Glöckner, Helge 9 Guo, Hongxin 9 Lu, Peng 9 Smoczyk, Knut 9 Topping, Peter Miles 9 Yau, Shing-Tung 8 Abolarinwa, Abimbola 8 Fang, Fuquan 8 Han, Xiaoli 8 Huang, Guangyue 8 Huisken, Gerhard 8 Jost, Jürgen 8 Korpinar, Talat 8 McCoy, James Alexander 8 Sinestrari, Carlo 8 Vazquez, Juan Luis 8 Wang, Linfeng 8 Ye, Rugang 8 Zhang, Yuguang 8 Zhang, Zhou 7 Bamler, Richard H. 7 Chen, Binglong 7 Colding, Tobias Holck 7 Fang, Shouwen 7 Hsu, Shu-Yu 7 Knüpfer, Hans 7 Li, Jiayu 7 Lott, John 7 Modin, Klas 7 Petersen, Peter V 7 Pop, Camelia Alexandra 7 Rong, Xiaochun 7 Shen, Yuliang 7 Song, Jian 7 Tannenbaum, Allen Robert 7 Wang, Bing 7 Wei, Yong 7 Yang, Yunlong 7 Zhang, Liangdi 7 Zhang, Xi 7 Zhu, Meng 6 Azami, Shahroud 6 Bauer, Martin 6 Bellettini, Giovanni 6 Bidabad, Behroz 6 Chen, Jingyi 6 Chou, Kai-Seng 6 Deng, Yuxing 6 Gao, Laiyuan 6 Giga, Yoshikazu 6 Grove, Karsten 6 Hou, Songbo 6 Ishida, Masashi 6 Knopf, Dan 6 Kotschwar, Brett L. 6 Kuczumow, Tadeusz 6 Li, Haozhao 6 Lin, Yu-Chu 6 Liu, Yannan 6 Minicozzi, William Philip II 6 Munteanu, Ovidiu 6 Petropoulou, Eugenia N. 6 Qu, Changzheng 6 Razavi, Asadollah 6 Savas-Halilaj, Andreas 6 Simon, Miles 6 Struwe, Michael 6 Tam, Luen-Fai ...and 1,981 more Authors
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#### Cited in 322 Serials

 97 The Journal of Geometric Analysis 94 Proceedings of the American Mathematical Society 91 Calculus of Variations and Partial Differential Equations 74 Journal of Mathematical Analysis and Applications 67 Transactions of the American Mathematical Society 65 Advances in Mathematics 61 Journal of Differential Equations 58 Journal of Geometry and Physics 58 Mathematische Annalen 53 Journal of Functional Analysis 51 Mathematische Zeitschrift 49 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 48 Annals of Global Analysis and Geometry 47 Inventiones Mathematicae 41 Communications in Mathematical Physics 39 Differential Geometry and its Applications 30 Geometriae Dedicata 28 Manuscripta Mathematica 27 Bulletin of the American Mathematical Society. New Series 26 Duke Mathematical Journal 25 Communications in Partial Differential Equations 24 Journal für die Reine und Angewandte Mathematik 24 Journal of the American Mathematical Society 24 Geometry & Topology 20 Journal of Mathematical Physics 20 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 19 Archive for Rational Mechanics and Analysis 19 International Journal of Mathematics 18 Comptes Rendus. Mathématique. Académie des Sciences, Paris 18 International Journal of Geometric Methods in Modern Physics 16 Communications on Pure and Applied Mathematics 16 Annali di Matematica Pura ed Applicata. Serie Quarta 16 Acta Mathematica Sinica. English Series 15 Science China. Mathematics 14 Results in Mathematics 14 Geometric and Functional Analysis. GAFA 14 Discrete and Continuous Dynamical Systems 14 Annals of Mathematics. Second Series 14 Nonlinear Analysis. Theory, Methods & Applications 13 Frontiers of Mathematics in China 12 Archiv der Mathematik 12 Tohoku Mathematical Journal. Second Series 12 Chinese Annals of Mathematics. Series B 12 Journal de Mathématiques Pures et Appliquées. Neuvième Série 11 Journal of Mathematical Sciences (New York) 11 Journal of the European Mathematical Society (JEMS) 11 Communications in Contemporary Mathematics 10 Journal of Evolution Equations 9 Journal of Computational Physics 9 Monatshefte für Mathematik 9 Siberian Mathematical Journal 9 Science in China. Series A 8 Israel Journal of Mathematics 8 Journal d’Analyse Mathématique 8 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 8 Journal of Geometry 8 NoDEA. Nonlinear Differential Equations and Applications 7 Acta Mathematica 7 Acta Applicandae Mathematicae 7 Japan Journal of Industrial and Applied Mathematics 7 Bulletin des Sciences Mathématiques 7 Journal of High Energy Physics 6 Mathematical Methods in the Applied Sciences 6 Journal of the Korean Mathematical Society 6 Mathematische Nachrichten 6 Topology and its Applications 6 Applied Mathematics Letters 6 Indagationes Mathematicae. New Series 6 Potential Analysis 6 Communications of the Korean Mathematical Society 6 Journal of Nonlinear Mathematical Physics 6 Journal of Geometric Mechanics 6 Communications in Mathematics and Statistics 6 Geometric Flows 5 Letters in Mathematical Physics 5 Rocky Mountain Journal of Mathematics 5 Reviews in Mathematical Physics 5 Annales de l’Institut Fourier 5 Kodai Mathematical Journal 5 Proceedings of the Japan Academy. Series A 5 Physica D 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 Communications on Pure and Applied Analysis 5 Bulletin of the Brazilian Mathematical Society. New Series 5 Mediterranean Journal of Mathematics 5 Advances in Mathematical Physics 5 Axioms 4 Bulletin of the Australian Mathematical Society 4 General Relativity and Gravitation 4 Mathematical Notes 4 Nonlinearity 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Publications Mathématiques 4 Memoirs of the American Mathematical Society 4 Pacific Journal of Mathematics 4 SIAM Journal on Mathematical Analysis 4 Stochastic Processes and their Applications 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 4 Acta Mathematica Sinica. New Series ...and 222 more Serials
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#### Cited in 54 Fields

 1,389 Differential geometry (53-XX) 758 Partial differential equations (35-XX) 612 Global analysis, analysis on manifolds (58-XX) 157 Several complex variables and analytic spaces (32-XX) 107 Manifolds and cell complexes (57-XX) 95 Dynamical systems and ergodic theory (37-XX) 83 Functional analysis (46-XX) 81 Functions of a complex variable (30-XX) 71 Quantum theory (81-XX) 69 Topological groups, Lie groups (22-XX) 66 Fluid mechanics (76-XX) 64 Operator theory (47-XX) 52 Calculus of variations and optimal control; optimization (49-XX) 52 Probability theory and stochastic processes (60-XX) 52 Relativity and gravitational theory (83-XX) 49 Numerical analysis (65-XX) 46 Convex and discrete geometry (52-XX) 39 Algebraic geometry (14-XX) 34 Ordinary differential equations (34-XX) 28 Algebraic topology (55-XX) 26 Nonassociative rings and algebras (17-XX) 24 Mechanics of particles and systems (70-XX) 22 Computer science (68-XX) 21 Statistical mechanics, structure of matter (82-XX) 19 Potential theory (31-XX) 17 Mechanics of deformable solids (74-XX) 14 Real functions (26-XX) 13 Biology and other natural sciences (92-XX) 11 General topology (54-XX) 10 Difference and functional equations (39-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Category theory; homological algebra (18-XX) 7 Geometry (51-XX) 7 Systems theory; control (93-XX) 7 Information and communication theory, circuits (94-XX) 6 History and biography (01-XX) 6 Number theory (11-XX) 6 Measure and integration (28-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Group theory and generalizations (20-XX) 5 Statistics (62-XX) 4 General and overarching topics; collections (00-XX) 4 Combinatorics (05-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Approximations and expansions (41-XX) 4 Astronomy and astrophysics (85-XX) 4 Operations research, mathematical programming (90-XX) 2 Mathematical logic and foundations (03-XX) 2 Associative rings and algebras (16-XX) 2 $$K$$-theory (19-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Optics, electromagnetic theory (78-XX) 1 Special functions (33-XX) 1 Geophysics (86-XX)

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