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

DOI10.1016/J.DIFGEO.2022.101924zbMath1507.53060arXiv2011.06757WikidataQ114190859 ScholiaQ114190859MaRDI QIDQ6353667

Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Yu Kawakami, Kotaro Yamada, Shoichi Fujimori, Seong-Deog Yang

Publication date: 12 November 2020

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.

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Non-Euclidean differential geometry (53A35)

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