Metric conformal structures and hyperbolic dimension

Igor Mineyev

doi:10.1090/S1088-4173-07-00165-8

Metric conformal structures and hyperbolic dimension

Igor Mineyev

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For any hyperbolic complex X and a ∈ X we construct a visual metric d = d_a on ∂X that makes the Isom(X)-action on ∂X bi-Lipschitz, Möbius, symmetric and conformal. We define a stereographic projection of d_a and show that it is a metric conformally equivalent to d_a. We also introduce a notion of hyperbolic dimension for hyperbolic spaces with group actions. Problems related to hyperbolic dimension are discussed.

Original language	English (US)
Pages (from-to)	137-163
Number of pages	27
Journal	Conformal Geometry and Dynamics
Volume	11
Issue number	11
DOIs	https://doi.org/10.1090/S1088-4173-07-00165-8
State	Published - Sep 12 2007

ASJC Scopus subject areas

Geometry and Topology

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10.1090/S1088-4173-07-00165-8

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Metric conformal structures and hyperbolic dimension

Abstract

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