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Remarks on Hamilton's compactness theorem for Ricci flow
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Topping, Peter (2014) Remarks on Hamilton's compactness theorem for Ricci flow. Journal für die reine und angewandte Mathematik (Crelles Journal), 2014 (692). pp. 173-191. doi:10.1515/crelle-2012-0079 ISSN 0075-4102.
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Official URL: http://dx.doi.org/10.1515/crelle-2012-0079
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.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Ricci flow, Riemannian manifolds | ||||||
| Journal or Publication Title: | Journal für die reine und angewandte Mathematik (Crelles Journal) | ||||||
| Publisher: | Walter de Gruyter GmbH | ||||||
| ISSN: | 0075-4102 | ||||||
| Official Date: | July 2014 | ||||||
| Dates: |
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| Volume: | 2014 | ||||||
| Number: | 692 | ||||||
| Page Range: | pp. 173-191 | ||||||
| DOI: | 10.1515/crelle-2012-0079 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 3 January 2018 | ||||||
| Date of first compliant Open Access: | 3 January 2018 | ||||||
| RIOXX Funder/Project Grant: |
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