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The canonical shrinking soliton associated to a Ricci flow
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Cabezas-Rivas, Esther and Topping, Peter (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. doi:10.1007/s00526-011-0407-x 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: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||||
Official Date: | January 2012 | ||||||
Dates: |
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Volume: | Vol.43 | ||||||
Number: | No.1-2 | ||||||
Page Range: | pp. 173-184 | ||||||
DOI: | 10.1007/s00526-011-0407-x | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access |
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