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arXiv · 2011.06757

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

Shoichi Fujimori·Yu Kawakami·Masatoshi Kokubu·Wayne Rossman·Masaaki Umehara·Kotaro Yamada·Seong-Deog Yang
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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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Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Kotaro Yamada, Seong-Deog Yang. 2020-11-13. Analytic extensions of constant mean curvature one geometric catenoids in de Sitter 3-space. https://arxiv.org/abs/2011.06757

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