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arXiv · 0807.4181

The canonical shrinking soliton associated to a Ricci flow

Esther Cabezas-Rivas·Peter M. Topping
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Abstract

To every Ricci flow on a manifold M over a time interval I, we associate a shrinking Ricci soliton on the space-time M x 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, and McCann and the second author; we briefly survey the link between these subjects.

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Esther Cabezas-Rivas, Peter M. Topping. 2009-11-26. The canonical shrinking soliton associated to a Ricci flow. https://arxiv.org/abs/0807.4181

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