Pressure gaps, geometric potentials, and nonpositively curved manifolds
Dynamical Systems
2025-06-24 v3 Differential Geometry
Abstract
In this paper, we derive a general pressure gap criterion for closed rank 1 manifolds whose singular sets are given by codimension 1 totally geodesic flat subtori. As an application, we show that under certain curvature constraints, potentials that decay faster than geometric potentials (towards to the singular set) have pressure gaps and have no phase transitions. Along the way, we prove that geometric potentials are H\"older continuous near singular sets.
Keywords
Cite
@article{arxiv.2209.05719,
title = {Pressure gaps, geometric potentials, and nonpositively curved manifolds},
author = {Dong Chen and Lien-Yung Kao and Kiho Park},
journal= {arXiv preprint arXiv:2209.05719},
year = {2025}
}
Comments
The Final version