Positive mass theorem with arbitrary ends and its application

TL;DR

This paper proves a positive mass theorem for asymptotically flat manifolds with arbitrary ends in dimensions up to seven and extends it to asymptotically locally Euclidean manifolds under certain conditions.

Contribution

It introduces a proof for the positive mass theorem applicable to manifolds with arbitrary ends and extends the result to locally Euclidean cases with incompressible conditions.

Findings

Positive mass theorem holds for manifolds with arbitrary ends in dimensions ≤7.

Extension of positive mass theorem to asymptotically locally Euclidean manifolds.

Establishment of conditions under which the theorem applies.

Abstract

In this article, we give a proof for positive mass theorem of asymptotically flat manifolds with arbitrary ends when the dimension is no greater than seven. As an application, we also show a positive mass theorem for asymptotically locally Euclidean manifolds with necessary incompressible conditions.