Harmonicity of quasiconformal measures and Poisson boundaries of hyperbolic spaces
| dc.creator | Connell, Chris | |
| dc.creator | Muchnik, Roman | |
| dc.date | 2004-08-25 | |
| dc.date.accessioned | 2026-07-07T05:11:34Z | |
| dc.date.available | 2026-07-07T05:11:34Z | |
| dc.description | We consider a group G of isometries acting on a (not necessarily geodesic) delta-hyperbolic space X and possessing a radial limit set of full measure within its limit set. For any continuous quasiconformal measure w supported on the limit set, we produce a stationary measure m on G. Moreover the limit set together with w forms a m-boundary and w is harmonic with respect to the random walk induced by m. In the case when X is a CAT(-1) space and G acts cocompactly, for instance, we show that m has finite first moment. This implies that the boundary of X with w is the unique Poisson boundary for m. As a bi-product, we establish sufficient conditions for a set of continuous functions to form a positive basis, either in the L^1 or sup norm, for the space of uniformly positive lower-semicontinuous functions on a general metric measure space. | |
| dc.description | 56 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408355 | |
| dc.identifier | http://arxiv.org/abs/math/0408355 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72287 | |
| dc.subject | Group Theory | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.subject | 60J50;20F67;37A35;41A65 | |
| dc.title | Harmonicity of quasiconformal measures and Poisson boundaries of hyperbolic spaces | |
| dc.type | text |