Work

Pressure gaps, geometric potentials, and nonpositively curved manifolds

Year: 2025

Type: article

Abstract: In this paper, we derive a general pressure gap criterion for closed rank 1 manifolds with singular sets characterized by codimension 1 totally geodesic flat subtori. As an application, we demonstrate that under specific curvature constraints, potentials that decay faster than geometric potentials (towards the singular set) exhibit pressure gaps and lack phase transitions. Additionally, we prove that geometric potentials are Hölder continuous near singular sets.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/9567

Authors: Dong Chen, Lien-Yung Kao, Kiho Park

Institutions: Indiana University Indianapolis, George Washington University, Korea Institute for Advanced Study

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Simons Foundation, Indiana University-Purdue University Indianapolis, National Center for Theoretical Sciences

Awards: G3065466221, G434646389, G4518884834, G871940946