Isoperimetry by stretching

TL;DR

This paper introduces a method to construct isoperimetric regions in closed manifolds using separating hypersurfaces, resulting in boundaries with diverse topologies and singularities.

Contribution

It provides a novel construction technique for isoperimetric regions that broadens the understanding of possible boundary topologies and singular sets.

Findings

Isoperimetric boundaries can have various topological types.

Construction method produces boundaries with singularities.

Expands known classes of isoperimetric regions.

Abstract

We construct isoperimetric regions from separating hypersurfaces in closed manifolds. This yields isoperimetric boundaries exhibiting a wide variety of topological types and singular sets.