Existence of isoperimetric regions in contact sub-Riemannian manifolds

TL;DR

This paper proves the existence of perimeter-minimizing regions with fixed volume in certain contact sub-Riemannian manifolds, extending geometric measure theory into this specialized setting.

Contribution

It establishes the existence of isoperimetric regions in contact sub-Riemannian manifolds under specific symmetry conditions, a novel result in geometric analysis.

Findings

Existence of isoperimetric regions proven in contact sub-Riemannian manifolds.

Results apply when the quotient by contact-preserving transformations is compact.

Advances understanding of geometric measure theory in sub-Riemannian geometry.

Abstract

We prove existence of regions minimizing perimeter under a volume constraint in contact sub-Riemannian manifolds such that their quotient by the group of contact transformations preserving the sub-Riemannian metric is compact.