Optimal Transport and Generalized Ricci Flow
Differential Geometry
2024-01-11 v2 Analysis of PDEs
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
Cite
@article{arxiv.2306.01649,
title = {Optimal Transport and Generalized Ricci Flow},
author = {Eva Kopfer and Jeffrey Streets},
journal= {arXiv preprint arXiv:2306.01649},
year = {2024}
}