English

Remarks on Hamilton's Compactness Theorem for Ricci flow

Differential Geometry 2011-10-18 v1 Analysis of PDEs

Abstract

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.

Keywords

Cite

@article{arxiv.1110.3714,
  title  = {Remarks on Hamilton's Compactness Theorem for Ricci flow},
  author = {Peter Topping},
  journal= {arXiv preprint arXiv:1110.3714},
  year   = {2011}
}

Comments

18 pages, 1 figure

R2 v1 2026-06-21T19:21:26.315Z