On the positive mass theorem for manifolds with corners

TL;DR

This paper investigates the positive mass theorem for manifolds with corners by smoothing metrics with Ricci flow, improving previous results and extending zero mass analysis to higher dimensions.

Contribution

It introduces a Ricci flow-based smoothing approach to analyze the positive mass theorem for non-smooth manifolds with corners, extending zero mass results to higher dimensions.

Findings

Improved understanding of ADM mass behavior under Ricci flow

Extended zero mass case analysis to higher-dimensional manifolds

Enhanced techniques for non-smooth metric analysis

Abstract

We study the positive mass theorem for certain non-smooth metrics following P. Miao's work. Our approach is to smooth the metric using the Ricci flow. As well as improving some previous results on the behaviour of the ADM mass under the Ricci flow, we extend the analysis of the zero mass case to higher dimensions.