Scalar curvature rigidity with a volume constraint

TL;DR

This paper proves a scalar curvature rigidity theorem for the hemisphere under volume constraints, inspired by a counterexample to Min-Oo's conjecture, advancing understanding of geometric rigidity.

Contribution

It introduces a volume constrained scalar curvature rigidity theorem specifically applicable to the hemisphere, addressing gaps highlighted by previous counterexamples.

Findings

Establishes a new rigidity theorem for the hemisphere with volume constraints.

Provides insights into scalar curvature behavior under geometric constraints.

Extends the scope of scalar curvature rigidity results.

Abstract

Motivated by Brendle-Marques-Neves' counterexample to the Min-Oo's conjecture, we prove a volume constrained scalar curvature rigidity theorem which applies to the hemisphere.