We introduce the notion of ℒ-optimal transportation, and use it to construct a natural monotonic quantity for Ricci flow which includes a selection of other monotonicity results, including some key discoveries of Perelman [The entropy formula for the Ricci flow and its geometric applications, 2002] (both related to entropy and to ℒ-length) and a recent result of McCann and the author [Topping, Amer. J. Math.].
© Walter de Gruyter Berlin · New York 2009