Scalar curvature rigidity of convex polytopes

TL;DR

This paper establishes a scalar curvature rigidity theorem for convex polytopes, utilizing Fredholm theory for Dirac operators and a variant of Fefferman-Phong's theorem to analyze geometric properties.

Contribution

It introduces a novel scalar curvature rigidity result for convex polytopes, applying advanced analytical techniques involving Dirac operators and boundary value problems.

Findings

Proves scalar curvature rigidity for convex polytopes

Develops a new application of Fredholm theory in geometric analysis

Highlights the role of Fefferman-Phong type theorems in boundary geometry

Abstract

We prove a scalar curvature rigidity theorem for convex polytopes. The proof uses the Fredholm theory for Dirac operators on manifolds with boundary. A variant of a theorem of Fefferman and Phong plays a central role in our analysis.