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The canonical shrinking soliton associated to a Ricci flow
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Cabezas-Rivas, Esther and Topping, Peter, 1971- (2012) The canonical shrinking soliton associated to a Ricci flow. Calculus of Variations and Partial Differential Equations, Vol.43 (No.1-2). pp. 173-184. ISSN 0944-2669
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Official URL: http://dx.doi.org/10.1007/s00526-011-0407-x
Abstract
To every Ricci flow on a manifold over a time interval IR−, we associate a shrinking Ricci soliton on the space–time I. We relate properties of the original Ricci flow to properties of the new higher-dimensional Ricci flow equipped with its own time-parameter. This geometric construction was discovered by consideration of the theory of optimal transportation, and in particular the results of the second author Topping (J Reine Angew Math 636:93–122, 2009), and McCann and the second author (Am J Math 132:711–730, 2010); we briefly survey the link between these subjects.
| Item Type: | Submitted Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
| Divisions: | Faculty of Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Ricci flow, Solitons |
| Journal or Publication Title: | Calculus of Variations and Partial Differential Equations |
| Publisher: | Springer |
| ISSN: | 0944-2669 |
| Date: | January 2012 |
| Volume: | Vol.43 |
| Number: | No.1-2 |
| Page Range: | pp. 173-184 |
| Identification Number: | 10.1007/s00526-011-0407-x |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/39049 |
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