On the isoperimetric problem in Euclidean space with density

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

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.
19 pages, 3 figures

Keywords

Differential Geometry, 49Q20; 53C17

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/108879

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0602135
 http://arxiv.org/abs/math/0602135

Collections

arXiv