Manhattan Curves for Hyperbolic Surfaces with Cusps
Dynamical Systems
2018-02-22 v2
Abstract
In this paper, we study an interesting curve, so-called the Manhattan curve, associated with a pair of boundary-preserving Fuchsian representations of a (non-compact) surface, especially representations corresponding to Riemann surfaces with cusps. Using Thermodynamic Formalism (for countable Markov shifts), we prove the analyticity of the Manhattan curve. Moreover, we derive several dynamical and geometric rigidity results, which generalize results of Marc Burger and Richard Sharp for convex-cocompact Fuchsian representations.
Cite
@article{arxiv.1801.09826,
title = {Manhattan Curves for Hyperbolic Surfaces with Cusps},
author = {Lien-Yung Kao},
journal= {arXiv preprint arXiv:1801.09826},
year = {2018}
}
Comments
34 pages and 2 figures. Minor changes, references updated