On the isoperimetric problem in Euclidean space with density |
| |
Authors: | César Rosales Antonio Cañete Vincent Bayle Frank Morgan |
| |
Institution: | (1) Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain;(2) Institute Fourier, BP 74, 38402 Saint Martin D’Heres Cedex, France;(3) Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA |
| |
Abstract: | 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 by using symmetrization techniques.
First and second authors are partially supported by MCyT-Feder research project MTM2004-01387, fourth author by the National
Science Foundation. |
| |
Keywords: | Manifolds with density Isoperimetric problem Generalized mean curvature Stability Symmetrization |
本文献已被 SpringerLink 等数据库收录! |
|