4 papers
Gaussian Volume Functional, Integral Scalar Curvature, and Minimal Super-Ricci Flows
Marco Flaim, Erik Hupp, Karl-Theodor Sturm
We present a synthetic notion of scalar curvature (and its integral) for Riemannian manifolds and metric measure spaces, defined in terms of the initial slope of a Gaussian (double…
Entropy and Fisher information in non-convex domains: one chain to rule them all
Jean-Baptiste Casteras, Marco Flaim, Léonard Monsaingeon
We prove that the (square root) Fisher information functional is a strong Wasserstein upper gradient of the entropy on non-convex Riemannian domains. This fills a gap in the litera…
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…
On a parabolic curvature lower bound generalizing Ricci flows
Marco Flaim, Erik Hupp
Optimal transport plays a major role in the study of manifolds with Ricci curvature bounded below. Some results in this setting have been extended to super Ricci flows, revealing a…