Mean Curvature of Hypersurfaces in Killing Submersions with Bounded\n Shadow

2017/12/20 by Vicent Gimeno, Gimeno, Vicent
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1712.07675

openalex publication_date 2017/12/20 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Given a complete hypersurface isometrically immersed in an ambient manifold,\nin this paper we provide a lower bound for the norm of the mean curvature\nvector field of the immersion assuming that:\n 1) The ambient manifold admits a Killing submersion with unit-length Killing\nvector field.\n 2)The projection of the image of the immersion is bounded in the base\nmanifold.\n 3)The hypersurface is stochastically complete, or the immersion is proper.\n

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