Rigidity of compact Riemannian spin Manifolds with Boundary

TL;DR

This paper establishes new rigidity theorems for compact Riemannian spin manifolds with boundary, focusing on scalar curvature bounds and extending previous results related to geometric conjectures.

Contribution

It generalizes existing rigidity results for manifolds with boundary under scalar curvature constraints, based on a conjecture by Schroeder and Strake.

Findings

New rigidity theorems for manifolds with scalar curvature bounded below by a non-positive constant.

Generalizations of Hang-Wang's results.

Connections to conjectures by Schroeder and Strake.

Abstract

In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake \cite{schroeder}.