Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 003, 15 pages      arXiv:2306.01649      https://doi.org/10.3842/SIGMA.2024.003
Contribution to the Special Issue on Differential Geometry Inspired by Mathematical Physics in honor of Jean-Pierre Bourguignon for his 75th birthday

Optimal Transport and Generalized Ricci Flow

Eva Kopfer a and Jeffrey Streets b
a) Institut für Angewandte Mathematik, Universität Bonn, 53115 Bonn, Germany
b) Rowland Hall, University of California, Irvine, CA, USA

Received June 06, 2023, in final form January 06, 2024; Published online January 10, 2024

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.

Key words: generalized Ricci flow; optimal transport.

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