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Lecture Notes on Gradient Flows and Optimal Transport

Published 20 Sep 2010 in math.CA, math.AP, math.DG, and math.PR | (1009.3737v1)

Abstract: We present a short overview on the strongest variational formulation for gradient flows of geodesically $\lambda$-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009.

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