103 citations · 140 across the 6 of their papers we have counts for
6 papers
Classification of compact ancient solutions to the Ricci flow on surfaces
Panagiota Daskalopoulos, Richard Hamilton, Natasa Sesum
We consider an ancient solution of the Ricci flow on a compact surface that exists for and becomes spherical at time . We prove that the metric…
Differential Harnack Estimates for Time-dependent Heat Equations with Potentials
Xiaodong Cao, Richard S. Hamilton
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positiv…
Classification of compact ancient solutions to the curve shortening flow
Panagiota Daskalopoulos, Richard Hamilton, Natasa Sesum
We consider an embedded convex ancient solution to the curve shortening flow in . We prove that there are only two possibilities: the family is either the…
Gaussian densities and stability for some Ricci solitons
Huai-Dong Cao, Richard S. Hamilton, Tom Ilmanen
In this announcement, we exhibit the second variation of Perelman's and functionals for the Ricci flow, and investigate the linear stability of examples. We also define the…
The Cross Curvature Flow of 3-manifolds with Negative Sectional Curvature
Bennett Chow, Richard Hamilton
We introduce a geometric evolution equation for 3-manifolds with sectional curvature of one sign which is in some sense dual to the Ricci flow. On a closed 3-manifold with negative…
Gradient Kähler-Ricci Solitons and Periodic Orbits
Huai-Dong Cao, Richard S. Hamilton
We study Hamiltonian dynamics of gradient Kaehler-Ricci solitons that arise as limits of dilations of singularities of the Ricci flow on compact Kaehler manifolds. Our main result…