Pressure metrics and Manhattan curves for Teichmüller spaces of punctured surfaces

2019/04/29 by Lien-Yung Kao, Kao, Lien-Yung · 1 citation
Mathematics · #30F60 #37D35 #37F30 #Analytic and geometric function theory #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1904.12429

openalex publication_date 2019/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend the construction of pressure metrics to Teichmüller spaces of surfaces with punctures. This construction recovers Thurston's Riemannian metric on Teichmüller spaces. Moreover, we prove the real analyticity and the convexity of Manhattan curves of the finite area type-preserving Fuchsian representations, and thus we obtain several related entropy rigidity results. Lastly, relating the two topics mentioned above, we show that one can derive the pressure metric by varying Manhattan curves.

Cited by

• Manhattan curves in complex dynamics and asymptotic correlation of multiplier spectra

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