3 papers
math.DG2025
Synthetic approaches to Ricci flows
Matthias Erbar, Marco Flaim, Eric Hupp +3
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 op…
math.DG2025
Synthetic notions of Ricci flow for metric measure spaces
Matthias Erbar, Zhenhao Li, Timo Schultz
We develop different synthetic notions of Ricci flow in the setting of time-dependent metric measure spaces based on ideas from optimal transport. They are formulated in terms of d…
math.AP2024
Covariance-modulated optimal transport and gradient flows
Martin Burger, Matthias Erbar, Franca Hoffmann +2
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics…