The canonical shrinking soliton associated to a Ricci flow
arXiv:0807.4181
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.
slight changes in hypotheses theorem 1.1, a sign corrected in Proposition 2.2, section 6 made more precise