Margulis Lemma on $\text{RCD}(K,N)$ spaces

TL;DR

This paper extends the Margulis Lemma to $ ext{RCD}(K,N)$ spaces, providing new regularity estimates for flows and broadening the understanding of geometric group theory in these metric measure spaces.

Contribution

The paper introduces an extension of the Margulis Lemma to $ ext{RCD}(K,N)$ spaces and develops improved regularity estimates for Regular Lagrangian flows in this setting.

Findings

Extended Margulis Lemma to $ ext{RCD}(K,N)$ spaces

Derived improved regularity estimates for flows

Enhanced understanding of geometric structures in metric measure spaces

Abstract

We extend the Margulis Lemma for manifolds with lower Ricci curvature bounds to the $\text{RCD}(K,N)$ setting. As one of our main tools, we obtain improved regularity estimates for Regular Langrangian flows on these spaces.