Boundary amenability of hyperbolic spaces
| dc.creator | Kaimanovich, Vadim A. | |
| dc.date | 2004-02-22 | |
| dc.date.accessioned | 2026-07-07T05:05:38Z | |
| dc.date.available | 2026-07-07T05:05:38Z | |
| dc.description | It is well-known that a Kleinian group is amenable if and only if it is elementary. We establish an analogous property for equivalence relations and foliations with Gromov hyperbolic leaves: they are amenable if and only if they are elementary in the sense that one can assign (in a measurable way) to any leaf a finite subset of its hyperbolic boundary (as in the group case, such subsets cannot actually contain more than 2 points). The analogous result for actions of word hyperbolic groups with a quasi-invariant measure is that such an action is amenable if and only if it factorizes through the hyperbolic boundary or its symmetric square. A byproduct of our approach is a proof of boundary amenability for isometry groups of Gromov hyperbolic spaces under the assumption that either the space is exponentially bounded or it is CAT(-1) and the group has a finite critical exponent. We also give examples showing that without these assumptions the boundary amenability may fail. | |
| dc.identifier | https://arxiv.org/abs/math/0402353 | |
| dc.identifier | http://arxiv.org/abs/math/0402353 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70239 | |
| dc.subject | Functional Analysis | |
| dc.subject | 37A20; 43A07; 53C99 | |
| dc.title | Boundary amenability of hyperbolic spaces | |
| dc.type | text |