Mass of $C^0$-asymptotically hyperbolic spaces via the normalized Ricci-DeTurck flow

TL;DR

This paper introduces a new mass function for asymptotically hyperbolic manifolds with continuous metrics using the normalized Ricci DeTurck flow, extending classical concepts to less regular settings.

Contribution

It defines a mass for continuous metrics on asymptotically hyperbolic spaces and proves its consistency with classical mass in smooth cases.

Findings

Mass function coincides with classical mass for smooth metrics

Established well-definedness of mass for continuous metrics

Introduced scalar curvature lower bound for continuous metrics

Abstract

We define a mass function on asymptotically hyperbolic manifolds with continuous metrics via the normalized Ricci DeTurck flow. This definition coincides with the classical mass for smooth metrics. We also introduce the scalar curvature lower bound for continuous metrics a key component in establishing the well-definedness of the continuous mass.