A Positive Mass Theorem on Asymptotically Hyperbolic Manifolds with Corners Along a Hypersurface

TL;DR

This paper proves a positive mass theorem for asymptotically hyperbolic spin manifolds with corners along a hypersurface, using integral representations and asymptotic analysis to understand mass changes under conformal transformations.

Contribution

It extends positive mass theorems to manifolds with corners along hypersurfaces, employing novel integral and asymptotic techniques for such geometries.

Findings

Established a positive mass theorem for manifolds with corners

Analyzed the impact of conformal changes on mass aspect

Developed integral representation methods for eigenfunction equations

Abstract

In this paper we take an approach similar to that in [M] to establish a positive mass theorem for asymptotically hyperbolic spin manifolds admitting corners along a hypersurface. The main analysis uses an integral representation of a solution to a perturbed eigenfunction equation to obtain an asymptotic expansion of the solution in the right order. This allows us to understand the change of the mass aspect of a conformal change of asymptotically hyperbolic metrics.