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math.DG2005
The rate of convergence of the mean curvature flow
Tom Ilmanen, Natasa Sesum
We study the flow of a smooth, strictly convex hypersurface by its mean curvature in . The surface remains smooth and convex, shrinking monotonically until…
math.DG2004★ 1 cited
Entropy and reduced distance for Ricci expanders
Michael Feldman, Tom Ilmanen, Lei Ni
Perelman has discovered two integral quantities, the shrinker entropy $\cW$ and the (backward) reduced volume, that are monotone under the Ricci flow $\pa g_{ij}/\pa t=-2R_{ij}$ an…
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…