Volume entropy rigidity of non-positively curved symmetric spaces

TL;DR

This paper characterizes symmetric spaces with non-positive curvature through the equality cases of geometric inequalities, providing a new rigidity criterion for such spaces.

Contribution

It introduces a novel rigidity characterization of non-positively curved symmetric spaces based on geometric inequality equalities.

Findings

Identifies conditions under which geometric inequalities become equalities in symmetric spaces.

Provides a new criterion for recognizing symmetric spaces of non-positive curvature.

Enhances understanding of geometric rigidity in non-positively curved spaces.

Abstract

We characterize symmetric spaces of non-positive curvature by the equality case of general inequalities between geometric quantities