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arXiv · 2209.05719

Pressure gaps, geometric potentials, and nonpositively curved manifolds

Dong Chen·Lien-Yung Kao·Kiho Park
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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.

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Dong Chen, Lien-Yung Kao, Kiho Park. 2022-09-13. Pressure gaps, geometric potentials, and nonpositively curved manifolds. https://arxiv.org/abs/2209.05719

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