Skin Structures in Scalar Curvature Geometry

TL;DR

This paper develops new methods using skin structures to analyze scalar curvature constraints on manifolds, avoiding traditional topological restrictions and integrating minimal hypersurface techniques with surgery.

Contribution

It introduces skin structures as a novel tool to derive obstruction and structure theories for scalar curvature without dimensional or topological limitations.

Findings

Established obstruction theories for scalar curvature using skin structures.

Unified minimal hypersurface methods with surgery techniques.

Extended scalar curvature analysis to broader classes of manifolds.

Abstract

This is the third in a series of papers on the geometry and analysis of singular area minimizing hypersurfaces. We show how to derive obstruction and structure theories for scalar curvature constraints without imposing dimensional or topological restrictions on the underlying manifold. To this end, we use skin structures to merge minimal hypersurface methods with surgery arguments.