Cheeger constants of surfaces and isoperimetric inequalities
| dc.creator | Papasoglu, Panos | |
| dc.date | 2007-06-29 | |
| dc.date.accessioned | 2026-07-07T08:13:10Z | |
| dc.date.available | 2026-07-07T08:13:10Z | |
| dc.description | We show that the Cheeger constant of compact surfaces is bounded by a function of the area. We apply this to isoperimetric profiles of bounded genus non-compact surfaces, to show that if their isoperimetric profile grows faster than $\sqrt t$, then it grows at least as fast as a linear function. This generalizes a result of Gromov for simply connected surfaces. We study the isoperimetric problem in dimension 3. We show that if the filling volume function in dimension 2 is Euclidean, while in dimension 3 is sub-Euclidean and there is a $g$ such that minimizers in dimension 3 have genus at most $g$, then the filling function in dimension 3 is `almost' linear. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/0706.4449 | |
| dc.identifier | http://arxiv.org/abs/0706.4449 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132704 | |
| dc.subject | Differential Geometry | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | Metric Geometry | |
| dc.subject | 53C20,53C23,20F65 | |
| dc.title | Cheeger constants of surfaces and isoperimetric inequalities | |
| dc.type | text |