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

• DOI: 10.48550/arxiv.math/0307217
• Publication Date: 2003-01-01
• Authors: Manuel Ritoré; César Rosales
• Keywords: Perimeter; Cone (formal languages); Convexity; Maxima and minima

We study the problem of existence regions separating a given amount volume with least possible perimeter inside Euclidean cone. Our main result shows that nonexistence for implies isoperimetric profile cone coincides one half-space. This allows us to give some criteria ensuring regions: instance, local convexity at boundary point. also characterize which are stable in convex cone, i.e., second order minima under constraint. From this it follows euclidean balls centered vertex intersected