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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Metric conformal structures and hyperbolic dimension


Author: Igor Mineyev
Journal: Conform. Geom. Dyn. 11 (2007), 137-163
MSC (2000): Primary 20F65, 20F67, 20F69, 37F35, 30C35, 54E35, 54E45, 51K99, 54F45
Published electronically: September 12, 2007
MathSciNet review: 2346214
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Abstract | References | Similar Articles | Additional Information

Abstract: For any hyperbolic complex $ X$ and $ a\in X$ we construct a visual metric  $ \check{d}=\check{d}_a$ on $ \partial X$ that makes the $ \operatorname{Isom}(X)$-action on $ \partial X$ bi-Lipschitz, Möbius, symmetric and conformal.

We define a stereographic projection of  $ \check{d}_a$ and show that it is a metric conformally equivalent to  $ \check{d}_a$.

We also introduce a notion of hyperbolic dimension for hyperbolic spaces with group actions. Problems related to hyperbolic dimension are discussed.


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Additional Information

Igor Mineyev
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
Email: mineyev@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S1088-4173-07-00165-8
PII: S 1088-4173(07)00165-8
Received by editor(s): May 7, 2007
Published electronically: September 12, 2007
Additional Notes: This project is partially supported by NSF CAREER grant DMS-0132514
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.