Optimal Transport and Generalized Ricci Flow

Eva Kopfer^a, Jeffrey Streets<sup>b

a</sup> Institut für Angewandte Mathematik, Universität Bonn, 53115 Bonn, Germany
^b Rowland Hall, University of California, Irvine, CA, USA

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.

Keywords: generalized Ricci flow, optimal transport.

MSC: 53E20, 49Q22

Received: June 6, 2023; in final form January 6, 2024; Published online January 10, 2024

Language: English

DOI: 10.3842/SIGMA.2024.003

ArXiv: 2306.01649