Compact anisotropic stable hypersurfaces with free boundary in convex solid cones

2023/02/13 by César Rosales, Rosales, César
Computer Science · Mathematics · #49Q20 #53C42 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2302.06538

openalex publication_date 2023/02/13 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28

Abstract

We consider a convex solid cone C⊂ℝⁿ⁺¹ with vertex at the origin and boundary \partialC smooth away from 0. Our main result shows that a compact two-sided hypersurface Σ immersed in C with free boundary in \partialC∖\0\ and minimizing, up to second order, an anisotropic area functional under a volume constraint is contained in a Wulff-shape.

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