On the topology of constant mean curvature surfaces in H2 X R with boundary in a plane

2019/07/22 by Vlad Moraru, Moraru, Vlad, Barbara Nelli +1
Mathematics · #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1907.09156

openalex publication_date 2019/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A gap in the proof prevents us to show that surfaces with constant mean curvature closed to 1/2 in H2 X R and having boundary with curvature greater than one, contained in a horizontal section P of H2 X R are topological disks, provided they are contained in one of the two halfspaces determined by P. This is the analogue in H2 X R of a result in R3 by A. Ros and H. Rosenberg [13, Theorem 2].

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