Analytic extensions of constant mean curvature one geometric catenoids in de Sitter 3-space. (English) Zbl 1507.53060
Examples of minimal surfaces in the Lorentz-Minkowski 3-space and surfaces of constant mean curvature in the de Sitter 3-space show that some of them admit non-trivial analytic extensions while some do not. The main goal of this paper is to clarify the notion of analytic completeness and derive certain useful criteria for such property to hold. The criteria is given in terms of a very weak notion of properness called arc-properness of continuous maps. These concepts are illustrated by a certain class of constant mean curvature surfaces called \(G\)-catenoids inside the de Sitter 3-space.
Reviewer: Martin Li (Hong Kong)
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 53A35 | Non-Euclidean differential geometry |
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