Optimal transport and generalized Ricci flow

Author:

Eva Kopfer, Jeffrey Streets

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Analysis of PDEs (math.AP)

journal:

date:

2023-06-01 16:00:00

Abstract

We prove results relating the theory of optimal transport and generalized Ricci flow. We define an adapted cost functional for measures using a solution of the associated dilaton flow. This determines a formal notion of geodesics in the space of measures, and we show geodesic convexity of an associated entropy functional. Finally we show monotonicity of the cost along the backwards heat flow, and use this to give a new proof of the monotonicity of the energy functional along generalized Ricci flow.

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