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Uniqueness and nonuniqueness for Ricci flow on surfaces : reverse cusp singularities
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Topping, Peter, 1971-. (2012) Uniqueness and nonuniqueness for Ricci flow on surfaces : reverse cusp singularities. International Mathematics Research Notices, Vol.2012 (No.10). pp. 2356-2376. ISSN 1073-7928
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Official URL: http://dx.doi.org/10.1093/imrn/rnr082
Abstract
We extend the notion of what it means for a complete Ricci flow to have a given initial metric, and consider the resulting well-posedness issues that arise in the two-dimensional case. On one hand, we construct examples of nonuniqueness by showing that surfaces with cusps can evolve either by keeping the cusps or by contracting them. On the other hand, by adding a noncollapsedness assumption for the initial metric, we establish a uniqueness result.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | International Mathematics Research Notices |
| Publisher: | Oxford University Press |
| ISSN: | 1073-7928 |
| Date: | 2012 |
| Volume: | Vol.2012 |
| Number: | No.10 |
| Number of Pages: | 21 |
| Page Range: | pp. 2356-2376 |
| Identification Number: | 10.1093/imrn/rnr082 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/44207 |
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