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Abstract
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.].
Received: 2007-11-22
Published Online: 2009-10-12
Published in Print: 2009-November
© Walter de Gruyter Berlin · New York 2009
