Uniqueness of H-surfaces in H²xR, |H| <= 1/2, with boundary one or two parallel horizontal circles

2007/03/02 by Barbara Nelli, B. Nelli, Ricardo Sá Earp +9
Mathematics · #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C42

paper · pdf · doi:10.48550/arxiv.math/0703054

19 pages

arxiv created 2007/03/02 · openalex publication_date 2007/03/02 · arxiv updated 2009/12/01 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We prove that a H-surface M in H²xR, |H| <= 1/2, inherits the symmetries of its boundary when the boundary is either a horizontal curve with curvature greater than one or two parallel horizontal curves with curvature greater than one, whose distance is greater or equal to πFurthermore we prove that the asymptotic boundary of a surface with mean curvature bounded away from zero consists of parts of straight lines, provided it is sufficiently regular

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