Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

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dc.creatorRitoré, Manuel
dc.creatorRosales, César
dc.date2003-07-16
dc.date.accessioned2026-07-07T04:59:41Z
dc.date.available2026-07-07T04:59:41Z
dc.descriptionWe 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.
dc.description21 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0307217
dc.identifierhttp://arxiv.org/abs/math/0307217
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68086
dc.subjectDifferential Geometry
dc.subject53C20 (Primary) 49Q20 (Secondary)
dc.titleExistence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones
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