Codimension 2 drawstrings with scalar curvature lower bounds

TL;DR

This paper introduces new Riemannian manifolds with scalar curvature bounds that collapse along codimension 2 submanifolds, providing insights into the stability of scalar curvature rigidity results like Llarull's Theorem and the Positive Mass Theorem.

Contribution

It constructs novel examples of manifolds with scalar curvature bounds exhibiting collapsing behavior, advancing understanding of scalar curvature rigidity stability.

Findings

New examples of manifolds with scalar curvature lower bounds

Collapse behavior along codimension 2 submanifolds demonstrated

Implications for stability of scalar curvature rigidity phenomena

Abstract

We produce new examples of Riemannian manifolds with scalar curvature lower bounds and collapsing behavior along codimension 2 submanifolds. Applications of this construction are given, primarily on questions concerning the stability of scalar curvature rigidity phenomena, such as Llarull's Theorem and the Positive Mass Theorem.