2022/09/13 by Dong Chen, Chen, Dong, Lien-Yung Kao +2
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2209.05719
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 Hölder continuous near singular sets.