Measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups

TL;DR

This paper proves that certain two-step sub-Riemannian structures and Lipschitz Carnot groups satisfy measure contraction properties, advancing understanding of geometric measure theory in these contexts.

Contribution

It establishes measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups, a novel result in geometric analysis.

Findings

Two-step sub-Riemannian structures satisfy measure contraction properties.

Lipschitz Carnot groups satisfy measure contraction properties.

Results apply to compact analytic manifolds with smooth measures.

Abstract

We prove that two-step analytic sub-Riemannian structures on a compact analytic manifold equipped with a smooth measure and Lipschitz Carnot groups satisfy measure contraction properties.