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math.DG2004★ 103 cited
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…
math.DG2003★ 11 cited
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…
math.DG1998
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…