Dirac and Plateau Billiards in Domains with Corners

TL;DR

This paper explores extending the concept of positive scalar curvature to domains with corners and singularities, analyzing metrics with positive scalar curvature in such complex geometric spaces.

Contribution

It proposes a framework for defining and studying positive scalar curvature metrics in domains with corners and singularities, expanding classical geometric analysis.

Findings

Extended positive scalar curvature concepts to singular spaces.

Identified conditions for metrics with positive scalar curvature in cornered domains.

Suggested potential applications in geometric analysis and mathematical physics.

Abstract

We study metrics with positive scalar curvatures in domains with corners and suggest possible extensions of the concept of positive scalar curvature to singular spaces.