Analytic extensions of constant mean curvature one geometric catenoids in de Sitter 3-space

2020/11/13 by Fujimori, Shoichi, Kawakami, Yu, Kokubu, Masatoshi +4
#53A10 #53A35 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.06757

Abstract

We show that a certain simply-stated notion of "analytic completeness" of the image of a real analytic map implies the map admits no analytic extension. We also give a useful criterion for that notion of analytic completeness by defining arc-properness of continuous maps, which can be considered as a very weak version of properness. As an application, we judge the analytic completeness of a certain class of constant mean curvature surfaces (the so-called "G-catenoids") or their analytic extensions in the de Sitter 3-space.

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