English

On the isoperimetric problem in Euclidean space with density

Differential Geometry 2007-05-23 v1

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(x2)\exp (|x|^2) by using symmetrization techniques.

Keywords

Cite

@article{arxiv.math/0602135,
  title  = {On the isoperimetric problem in Euclidean space with density},
  author = {César Rosales and Antonio Cañete and Vincent Bayle and Frank Morgan},
  journal= {arXiv preprint arXiv:math/0602135},
  year   = {2007}
}

Comments

19 pages, 3 figures