A note on the positive mass theorem with boundary

TL;DR

This paper discusses how existing results can be used to prove versions of the positive mass theorem for initial data sets with boundary in dimensions less than 8.

Contribution

It clarifies the application of established results to positive mass theorem variants involving boundaries in low dimensions.

Findings

Positive mass theorem holds for initial data sets with boundary in dimensions less than 8.

Utilizes existing results to establish new versions of the theorem.

Provides a simplified proof approach for boundary cases.

Abstract

In this short note we explain how one can use established results to prove various versions of the positive mass theorem for initial data sets with boundary, in dimensions less than 8.