Richard S. Hamilton | Academic Influence

Why Is Richard S. Hamilton Influential?

According to Wikipedia, Richard Streit Hamilton is Davies Professor of Mathematics at Columbia University, and is known for contributions to geometric analysis and partial differential equations. He is best known for foundational contributions to the theory of the Ricci flow and the development of a corresponding program of techniques and ideas for resolving the Poincaré conjecture and geometrization conjecture in the field of geometric topology. Grigori Perelman built upon Hamilton's results to prove the conjectures, and was awarded a Millennium Prize for his work. However, he declined the award, regarding Hamilton's contribution as being equal to his own.

Richard S. Hamilton's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Papers

Three-manifolds with positive Ricci curvature (2445)
The heat equation shrinking convex plane curves (1152)
The inverse function theorem of Nash and Moser (1110)
The Ricci flow on surfaces (871)
Four-manifolds with positive curvature operator (715)
The formations of singularities in the Ricci Flow (654)
Harmonic Maps of Manifolds with Boundary (389)
The Harnack estimate for the Ricci flow (356)
A Compactness Property for Solutions of the Ricci Flow (338)
Matrix Harnack estimate for the heat equation (291)
Harnack estimate for the mean curvature flow (211)
Four-manifolds with positive isotropic curvature (208)
Non-singular solutions of the Ricci flow on three-manifolds (176)
Eternal solutions to the Ricci flow (131)
EXTREMAL QUASICONFORMAL MAPPINGS WITH PRESCRIBED BOUNDARY VALUES (117)
On riemannian metrics adapted to three-dimensional contact manifolds (112)
Gaussian densities and stability for some Ricci solitons (111)
Constrained and linear Harnack inequalities for parabolic equations (91)
Differential Harnack Estimates for Time-Dependent Heat Equations with Potentials (84)
Monotonicity formulas for parabolic flows on manifolds (83)
A xed point theorem for holomorphic mappings (68)
Classification of compact ancient solutions to the curve shortening flow (62)
Classification of ancient compact solutions to the Ricci flow on surfaces (51)
ISOPERIMETRIC ESTIMATES FOR THE CURVE SHRINKING FLOW IN THE PLANE (50)
Deformation of complex structures on manifolds with boundary. I. The stable case (42)
The Ricci Curvature Equation (37)
Convex hypersurfaces with pinched second fundamental form (36)
AN ISOPERIMETRIC ESTIMATE FOR THE RICCI FLOW ON THE TWO-SPHERE (31)
Gradient K\"ahler-Ricci Solitons and Periodic Orbits (30)
The Cross Curvature Flow of 3-manifolds with Negative Sectional Curvature (26)
Quasi-convergence of Ricci flow for a class of metrics (25)
Classification of compact ancient solutions to the Ricci flow on surfaces (22)
The formation of singularities in the harmonic map heat flow (21)
Remarks on the entropy and Harnack estimates for the Gauss curvature flow (19)
Deformation of complex structures on manifolds with boundary. II. Families of noncoercive boundary value problems (18)
C ∞-REGULARITY OF THE INTERFACE OF THE EVOLUTION P-LAPLACIAN EQUATION (10)
The Harnack estimate for the Ricci flow on a surface — revisited (10)
Harmonic Mean Curvature Flow on Surfaces of Negative Gaussian Curvature (8)
$C^\infty$-regularity of the interface of the evolution p-laplacian equation (8)
THE GEOMETRIZATION CONJECTURE AFTER (3)
Survey on Discrete Ricci Flow (1)
SURFACES CONTRACTING BY |A | 2 (1)
Non-hyperelliptic Riemann surfaces (1)
THE RICCI FLOW ON SURFACES AND THE UNIFORMIZATION THEOREM (1)
Semi-elliptic and parabolic equations (0)
Workshop on Geometric Flows (0)
The heat equation for manifolds (0)
Growth estimates and convergence (0)
Regularity theorems for partial differential operators (0)

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