Portal de Periódicos da CAPES

On the isoperimetric problem in Euclidean space with density

2007; Springer Science+Business Media; Volume: 31; Issue: 1 Linguagem: Inglês

10.1007/s00526-007-0104-y

1432-0835

César Rosales, Antonio Cañete, Vincent Bayle, Frank Morgan,

Geometric Analysis and Curvature Flows

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.