The canonical shrinking soliton associated to a Ricci flow

To every Ricci flow on a manifold over a time interval , we associate a shrinking Ricci soliton on the space–time . 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...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2012, Vol.43 (1-2), p.173-184
Main Authors: Cabezas-Rivas, Esther, Topping, Peter M.
Format: Article
Language:English
Subjects:
Analysis
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Intervals
Links
Manifolds
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Optimization
Solitons
Systems Theory
Theoretical
Topological manifolds
Transportation
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Summary:To every Ricci flow on a manifold over a time interval , we associate a shrinking Ricci soliton on the space–time . 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.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-011-0407-x