Pressure metrics for deformation spaces of quasifuchsian groups with parabolics

Harrison Bray; Richard Canary; Lien-Yung Kao

doi:10.2140/agt.2023.23.3615

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arXiv · 2006.06184

Pressure metrics for deformation spaces of quasifuchsian groups with parabolics

Harrison Bray·Richard Canary·Lien-Yung Kao

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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).

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Harrison Bray, Richard Canary, Lien-Yung Kao. 2020-06-11. Pressure metrics for deformation spaces of quasifuchsian groups with parabolics. https://doi.org/10.2140/agt.2023.23.3615

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