  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.
