Scalar curvature bounds for 3D continuous metrics through the Inverse Mean Curvature Flow

TL;DR

This paper introduces a new way to define scalar curvature bounds in 3D manifolds with continuous metrics using inverse mean curvature flow, and proves a stability theorem for nonnegative scalar curvature in this setting.

Contribution

It develops a novel notion of scalar curvature bounds for continuous metrics via Hawking mass monotonicity along IMCF and establishes a related stability theorem.

Findings

Defined scalar curvature bounds for $C^0$ metrics using IMCF.

Proved a stability theorem for nonnegative scalar curvature in this context.

Abstract

We propose a notion of scalar curvature lower bounds in a three-dimensional Riemannian manifold endowed with a $C^0$ metric based on the monotonicity of the Hawking mass along the inverse mean curvature flow. We present a stability theorem for continuous Riemannian metrics with nonnegative scalar curvature in such IMCF sense.