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Pressure metrics for deformation spaces of quasifuchsian groups with parabolics

Harrison Bray, Richard Canary and Lien-Yung Kao

Algebraic & Geometric Topology 23 (2023) 3615–3653
Abstract

We produce a mapping class group–invariant pressure metric on the space QF (S) of quasiconformal deformations of a cofinite-area fuchsian group uniformizing 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.

Keywords
quasifuchsian groups, pressure metric, entropy
Mathematical Subject Classification
Primary: 57K32
References
Publication
Received: 6 August 2021
Revised: 13 December 2021
Accepted: 11 January 2022
Published: 5 November 2023
Authors
Harrison Bray
Department of Mathematics
George Mason University
Fairfax, VA
United States
Richard Canary
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States
Lien-Yung Kao
Department of Mathematics
George Washington University
Washington, DC
United States

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