Compact stable hypersurfaces with free boundary in convex solid cones\n with homogeneous densities

2013/04/04 by Antonio Cañete, Cañete, Antonio, César Rosales +1 · 1 citation
Computer Science · Mathematics · #53A10 (Secondary) #53C42 (Primary) #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1304.1438

openalex publication_date 2013/04/04 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We consider a smooth Euclidean solid cone endowed with a smooth homogeneous\ndensity function used to weight Euclidean volume and hypersurface area. By\nassuming convexity of the cone and a curvature-dimension condition we prove\nthat the unique compact, orientable, second order minima of the weighted area\nunder variations preserving the weighted volume and with free boundary in the\nboundary of the cone are intersections with the cone of round spheres centered\nat the vertex.\n

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