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Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones |
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| Authors: | Manuel Ritoré Cé sar Rosales |
| Affiliation: | Departamento de Geometría y Topología, Universidad de Granada, E--18071 Granada, Spain ; Departamento de Geometría y Topología, Universidad de Granada, E--18071 Granada, Spain |
| Abstract: | We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point. We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone. |
| Keywords: | Isoperimetric regions stability hypersurfaces with constant mean curvature |
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