ar X iv : 0 80 7 . 41 81 v 1 [ m at h . D G ] 2 5 Ju l 2 00 8 the canonical shrinking soliton associated to a ricci flow
نویسنده
چکیده
To every Ricci flow on a manifold M over a time interval I ⊂ R, we associate a shrinking Ricci soliton on the space-time M×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 [16], and McCann and the second author [10]; we briefly survey the link between these subjects.
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