Remarks on Hamilton's Compactness Theorem for Ricci flow

Details Remarks on Hamilton's Compactness Theorem for Ricci flow Remarks on Hamilton's Compactness Theorem for Ricci flow

2011-10-17

arxiv.org/abs/1110.3714v1

Mathematics

Differential Geometry

18 pages, 1 figure

Scientific paper

A fundamental tool in the analysis of Ricci flow is a compactness result of Hamilton in the spirit of the work of Cheeger, Gromov and others. Roughly speaking it allows one to take a sequence of Ricci flows with uniformly bounded curvature and uniformly controlled injectivity radius, and extract a subsequence that converges to a complete limiting Ricci flow. A widely quoted extension of this result allows the curvature to be bounded uniformly only in a local sense. However, in this note we give a counterexample.

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