Synthetic approaches to Ricci flows
Differential Geometry
2025-11-17 v1
Abstract
We review different notions of synthetic Ricci flow that apply to time-dependent families of metric measure spaces and which are based on properties of the heat flow, ideas from optimal transport, and the asymptotic behaviour of volumes. Each notion equivalently characterises (weighted) Ricci flow for smooth families of weighted Riemannian manifolds. We discuss the features of the different notions on various examples.
Keywords
Cite
@article{arxiv.2511.11477,
title = {Synthetic approaches to Ricci flows},
author = {Matthias Erbar and Marco Flaim and Eric Hupp and Zhenhao Li and Timo Schultz and Karl-Theodor Sturm},
journal= {arXiv preprint arXiv:2511.11477},
year = {2025}
}