Conformal measures associated to ends of hyperbolic n-manifolds
| dc.creator | Anderson, James W. | |
| dc.creator | Falk, Kurt | |
| dc.creator | Tukia, Pekka | |
| dc.date | 2004-09-29 | |
| dc.date | 2005-06-13 | |
| dc.date.accessioned | 2026-07-07T05:12:42Z | |
| dc.date.available | 2026-07-07T05:12:42Z | |
| dc.description | Let Gamma be a non-elementary Kleinian group acting on the closed n-dimensional unit ball and assume that its Poincare series converges at the exponent alpha. Let M_Gamma be the Gamma-quotient of the open unit ball. We consider certain families E = {E_1,...,E_p} of open subsets of M_Gamma such that M_Gamma minus the union of all E_i is compact. The sets E_i are called ends of M_Gamma and E is called a complete collection of ends for M_Gamma. We show that we can associate to each end in E a conformal measure of dimension alpha such that the two measures corresponding to different ends are mutually singular if non-trivial. Each conformal measure for Gamma of dimension alpha on the limit set Lambda(Gamma) of Gamma can be written as a sum of such conformal measures associated to ends in E. In dimension 3, our results overlap with some results of Bishop and Jones. | |
| dc.description | 23 pages, submitted to Quart. J. Math | |
| dc.identifier | https://arxiv.org/abs/math/0409582 | |
| dc.identifier | http://arxiv.org/abs/math/0409582 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72677 | |
| dc.subject | Complex Variables | |
| dc.subject | Geometric Topology | |
| dc.subject | 30F40 (Primary) 37F30, 37F35, 57M50, 30F45 (Secondary) | |
| dc.title | Conformal measures associated to ends of hyperbolic n-manifolds | |
| dc.type | text |