The canonical shrinking soliton associated to a Ricci flow

Details The canonical shrinking soliton associated to a Ricci flow The canonical shrinking soliton associated to a Ricci flow

2008-07-25

arxiv.org/abs/0807.4181v2

Mathematics

Differential Geometry

slight changes in hypotheses theorem 1.1, a sign corrected in Proposition 2.2, section 6 made more precise

Scientific paper

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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