Volume of spheres in doubling metric measured spaces and in groups of polynomial growth
| dc.creator | Tessera, R. | |
| dc.date | 2005-06-17 | |
| dc.date | 2008-11-17 | |
| dc.date.accessioned | 2026-07-07T10:18:29Z | |
| dc.date.available | 2026-07-07T10:18:29Z | |
| dc.description | Let G be a compactly generated locally compact group and let $U$ be a compact generating set. We prove that if G has polynomial growth, then (U^n) is a Folner sequence: that is, the volume of the boundary of U^n divided by U^n goes to zero. Moreover, we give a polynomial estimate of this ratio. Our proof is based on doubling property. As a matter of fact, the result remains true in a wide class of doubling metric measured spaces including manifolds and graphs. As an application, we obtain a balls averages L^p-pointwise ergodic theorem for probability G-spaces, with G of polynomial growth and for all p greater than 1. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0506362 | |
| dc.identifier | http://arxiv.org/abs/math/0506362 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174203 | |
| dc.subject | Group Theory | |
| dc.subject | Metric Geometry | |
| dc.title | Volume of spheres in doubling metric measured spaces and in groups of polynomial growth | |
| dc.type | text |