Optimal transport and Perelman’s reduced volume

By J. Lott. 2008

72 citations recorded by the source corpus.

We show that a certain entropy-like function is convex, under an optimal transport problem that is adapted to Ricci flow. We use this to reprove the monotonicity of Perelman’s reduced volume.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/c5832c8922702cbf2f7fa2d04a577343931a2100

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In Applied Mathematics

Citations in the corpus

Optimal transportation, topology and uniqueness (2010, background): “The first problem has become classical in the calculus of variations; it has deep connections to analysis [30,51,73,74,98], geometry [29,63,70,71,79,83,95,104], dynamics [7,10,59,82] and nonlinear partial differential equations [18,20,21,36,42, 72,102], as well as applications in physics [38,75,97],”
Five lectures on optimal transportation: Geometry, regularity and applications (2010, background): “It also guarantees almost everywhere differentiability of G by Alexandrov’s theorem (or by Lebesgue’s theorem in one dimension); see Theorem 3.2 for the sketch of a proof.”
Wasserstein geometry of Gaussian measures (2011, background): “The wide recogn ition of Wasserstein geometry defined on the space of Borel measures on a given metric sp ace, on the other hand, is a more recent phenomenon, excited by some important advan ces made by Brenier [4] and McCann [16] in the 90’s, and also implicit in Perelman’ s work [23] on Ricci flow”