Large scale Sobolev inequalities on metric measure spaces and applications
| dc.creator | Tessera, Romain | |
| dc.date | 2007-02-25 | |
| dc.date.accessioned | 2026-07-07T07:48:49Z | |
| dc.date.available | 2026-07-07T07:48:49Z | |
| dc.description | We introduce a notion of "gradient at a given scale" of functions defined on a metric measure space. We then use it to define Sobolev inequalities at large scale and we prove their invariance under large-scale equivalence (maps that generalize the quasi-isometries). We prove that for a Riemmanian manifold satisfying a local Poincare inequality, our notion of Sobolev inequalities at large scale is equivalent to its classical version. These notions provide a natural and efficient point of view to study the relations between the large time on-diagonal behavior of random walks and the isoperimetry of the space. Specializing our main result to locally compact groups, we obtain that the L^p-isoperimetric profile, for every p \in [1,\infty] is invariant under quasi-isometry between amenable unimodular compactly generated locally compact groups. A qualitative application of this new approach is a very general characterization of the existence of a spectral gap on a quasi-transitive measure space X, providing a natural point of view to understand this phenomenon. | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702751 | |
| dc.identifier | http://arxiv.org/abs/math/0702751 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124632 | |
| dc.subject | Metric Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 51F99; 43A85 | |
| dc.title | Large scale Sobolev inequalities on metric measure spaces and applications | |
| dc.type | text |