Remarks on a scalar curvature rigidity theorem of Brendle and Marques

TL;DR

This paper discusses an extension of Brendle and Marques's scalar curvature rigidity theorem, showing it remains valid on larger geodesic balls than previously established.

Contribution

It extends the known validity range of the scalar curvature rigidity theorem to larger geodesic balls.

Findings

The theorem holds on geodesic balls larger than previously proven.

The paper provides remarks that support this extended validity.

It clarifies conditions under which the rigidity theorem applies.

Abstract

In this paper, we provide some remarks on the scalar curvature rigidity theorem of Brendle and Marques in \cite{BrendleMarques}. The main result is that Brendle and Marques' theorem holds on a geodesic ball larger than that specified in [2].