On the isoperimetric problem in Euclidean space with density
| dc.creator | Rosales, César | |
| dc.creator | Cañete, Antonio | |
| dc.creator | Bayle, Vincent | |
| dc.creator | Morgan, Frank | |
| dc.date | 2006-02-07 | |
| dc.date.accessioned | 2026-07-07T07:03:11Z | |
| dc.date.available | 2026-07-07T07:03:11Z | |
| dc.description | We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive stability conditions, which lead to the conjecture that for a radial log-convex density, balls about the origin are isoperimetric regions. Finally, we prove this conjecture and the uniqueness of minimizers for the density $\exp (|x|^2)$ by using symmetrization techniques. | |
| dc.description | 19 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0602135 | |
| dc.identifier | http://arxiv.org/abs/math/0602135 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108879 | |
| dc.subject | Differential Geometry | |
| dc.subject | 49Q20; 53C17 | |
| dc.title | On the isoperimetric problem in Euclidean space with density | |
| dc.type | text |