Integral formulas for hypersurfaces in cones and related questions

2025/04/17 by Filomena Pacella, Pacella, Filomena, Giulio Tralli +1
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2504.13137

Abstract

We discuss the validity of Minkowski integral identities for hypersurfaces inside a cone, intersecting the boundary of the cone orthogonally. In doing so we correct a formula provided in [3]. Then we study rigidity results for constant mean curvature graphs proving the precise statement of a result given in [9] and [10]. Finally we provide an integral estimate for stable constant mean curvature hypersurfaces in cones.

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