Nonnegatively curved hypersurfaces with free boundary on a sphere

2017/07/11 by Mohammad Ghomi, Changwei Xiong, Ghomi, Mohammad +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1707.03323

Abstract

We prove that in Euclidean space Rⁿ⁺¹ any compact immersed nonnegatively curved hypersurface M with free boundary on the sphere Sⁿ is an embedded convex topological disk. In particular, when the m^th mean curvature of M is constant, for any 1≤ m≤ n, M is a spherical cap or an equatorial disk.

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