Some isoperimetric comparison theorems for convex bodies in Riemannian manifolds
| dc.creator | Bayle, Vincent | |
| dc.creator | Rosales, César | |
| dc.date | 2003-11-18 | |
| dc.date.accessioned | 2026-07-07T05:03:00Z | |
| dc.date.available | 2026-07-07T05:03:00Z | |
| dc.description | We prove that the isoperimetric profile of a convex domain $Ω$ with compact closure in a Riemannian manifold $(M^{n+1},g)$ satisfies a second order differential inequality which only depends on the dimension of the manifold and on a lower bound on the Ricci curvature of $Ω$. Regularity properties of the profile and topological consequences on isoperimetric regions arise naturally from this differential point of view. Moreover, by integrating the differential inequality we obtain sharp comparison theorems: not only can we derive an inequality which should be compared with Lévy-Gromov Inequality but we also show that if $\text{Ric}\geq nδ$ on $Ω$, then the profile of $Ω$ is bounded from above by the profile of the half-space $\mathbb{H}_δ^{n+1}$ in the simply connected space form with constant sectional curvature $δ$. As consequence of isoperimetric comparisons we obtain geometric estimations for the volume and the diameter of $Ω$, and for the first non-zero Neumann eigenvalue for the Laplace operator on $Ω$. | |
| dc.description | 19 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0311304 | |
| dc.identifier | http://arxiv.org/abs/math/0311304 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69240 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C20 (Primary) 49Q20 (Secondary) | |
| dc.title | Some isoperimetric comparison theorems for convex bodies in Riemannian manifolds | |
| dc.type | text |