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Conformal measures associated to ends of hyperbolic n-manifolds

Conformal measures associated to ends of hyperbolic n-manifolds
Conformal measures associated to ends of hyperbolic n-manifolds
Let G be a non-elementary Kleinian group acting on the closed n-dimensional unit ball and assume that its Poincare series converges at the exponent a. Let M be the G-quotient of the open unit ball. We consider certain families E={e1, ..., ep} of open subsets of M such that the complement of the union of e1, ..., ep in M is compact. The sets e1, ..., ep are the ends of M and E is a complete collection of ends for M. We associate to each end e in E an a-conformal measure such that the measures corresponding to different ends are mutually singular if non-trivial. Additionally, each a-conformal measure for G on its limit set can be written as a sum of such conformal measures associated to ends e in E. In dimension 3, our results overlap with some results of Bishop and Jones.
0033-5606
1-15
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Falk, Kurt
42ccda05-d800-4423-aaf3-a0e4f1f0bd13
Tukia, Pekka
97737653-8a0a-495e-be04-92f2d42f5257
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Falk, Kurt
42ccda05-d800-4423-aaf3-a0e4f1f0bd13
Tukia, Pekka
97737653-8a0a-495e-be04-92f2d42f5257

Anderson, James W., Falk, Kurt and Tukia, Pekka (2007) Conformal measures associated to ends of hyperbolic n-manifolds. The Quarterly Journal of Mathematics, 58 (1), 1-15. (doi:10.1093/qmath/hal019).

Record type: Article

Abstract

Let G be a non-elementary Kleinian group acting on the closed n-dimensional unit ball and assume that its Poincare series converges at the exponent a. Let M be the G-quotient of the open unit ball. We consider certain families E={e1, ..., ep} of open subsets of M such that the complement of the union of e1, ..., ep in M is compact. The sets e1, ..., ep are the ends of M and E is a complete collection of ends for M. We associate to each end e in E an a-conformal measure such that the measures corresponding to different ends are mutually singular if non-trivial. Additionally, each a-conformal measure for G on its limit set can be written as a sum of such conformal measures associated to ends e in E. In dimension 3, our results overlap with some results of Bishop and Jones.

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Published date: March 2007
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 44636
URI: https://eprints.soton.ac.uk/id/eprint/44636
ISSN: 0033-5606
PURE UUID: b73edeb8-3630-42b8-8f40-862d0d56e917
ORCID for James W. Anderson: ORCID iD orcid.org/0000-0002-7849-144X

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Date deposited: 06 Mar 2007
Last modified: 07 Aug 2019 00:50

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Author: Kurt Falk
Author: Pekka Tukia

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