A Ricci flow proof of a result by Gromov on lower bounds for scalar curvature

TL;DR

This paper presents a new proof of Gromov's theorem on the stability of scalar curvature lower bounds under $C^0$-convergence, utilizing Ricci flow techniques to provide a different perspective on the result.

Contribution

The paper introduces a Ricci flow-based proof of Gromov's theorem, offering a novel approach to understanding scalar curvature stability.

Findings

Scalar curvature lower bounds are stable under $C^0$-convergence.

Ricci flow can be effectively used to reprove geometric theorems.

The proof provides new insights into the behavior of scalar curvature.

Abstract

In this note we reprove a theorem of Gromov using Ricci flow. The theorem states that a, possibly non-constant, lower bound on the scalar curvature is stable under $C^0$-convergence of the metric.