On the isoperimetric problem in Euclidean space with density
We study the isoperimetric problemfor Euclidean space endowedwith 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...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2008 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/110286 |
| Acceso en línea: | https://hdl.handle.net/11441/110286 https://doi.org/10.1007/s00526-007-0104-y |
| Access Level: | acceso abierto |
| Palabra clave: | Manifolds with density Isoperimetric problem Generalized mean curvature Stability Symmetrization |
| Sumario: | We study the isoperimetric problemfor Euclidean space endowedwith 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. |
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