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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
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…