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math.DG2026
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…
math.DG2025
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…
math.DG2023★ 4 cited
Lower Ricci Curvature and Nonexistence of Manifold Structure
Erik Hupp, Aaron Naber, Kai-Hsiang Wang
It is known that a limit of manifolds with uniform lower bounds on Ricci curvature must be -rectifiable for some unique $\dim X:= k\leq n = \dim M…