103 citations · 109 across the 3 of their papers we have counts for
3 papers
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…
math.DG2002★ 5 cited
A lower bound for the diameter of solutions to the Ricci flow with nonzero
Tom Ilmanen, Dan Knopf
We obtain a lower bound for the diameter of a solution to the Ricci flow on a compact manifold with nonvanishing first real cohomology. A consequence of our result is an affirmativ…