Pressure metrics for deformation spaces of quasifuchsian groups with parabolics
Geometric Topology
2023-11-15 v3 Dynamical Systems
Abstract
In this paper, we produce a mapping class group invariant pressure metric on the space QF(S) of quasiconformal deformations of a co-finite area Fuchsian group uniformizing a surface S. Our pressure metric arises from an analytic pressure form on QF(S) which is degenerate only on pure bending vectors on the Fuchsian locus. Our techniques also show that the Hausdorff dimension of the limit set varies analytically over QF(S).
Keywords
Cite
@article{arxiv.2006.06184,
title = {Pressure metrics for deformation spaces of quasifuchsian groups with parabolics},
author = {Harrison Bray and Richard Canary and Lien-Yung Kao},
journal= {arXiv preprint arXiv:2006.06184},
year = {2023}
}