A lower bound for the diameter of solutions to the Ricci flow with nonzero $H^{1}(M^{n};R)$

Tom Ilmanen; Dan Knopf

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A lower bound for the diameter of solutions to the Ricci flow with nonzero $H^{1}(M^{n};R)$

Tom Ilmanen·Dan Knopf

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Abstract

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 affirmative answer to Hamilton's conjecture that a product metric on $(S^{1}\times S^{n-1}$ cannot arise as a final time limit flow.

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BibTeX RIS

Tom Ilmanen, Dan Knopf. 2002-11-14. A lower bound for the diameter of solutions to the Ricci flow with nonzero $H^{1}(M^{n};R)$. https://arxiv.org/abs/math/0211230

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