The canonical shrinking soliton associated to a Ricci flow

Cabezas-Rivas, Esther; Topping, Peter
January 2012
Calculus of Variations & Partial Differential Equations;Jan2012, Vol. 43 Issue 1/2, p173
Academic Journal
To every Ricci flow on a manifold $${\mathcal{M}}$$ over a time interval $${I\subset\mathbb{R}_-}$$, we associate a shrinking Ricci soliton on the space-time $${\mathcal{M}\times I}$$. 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, ), and McCann and the second author (Am J Math 132:711-730, ); we briefly survey the link between these subjects.


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