Analytic extension of exceptional constant mean curvature one catenoids in de Sitter 3-space

2015/07/23 by Shoichi Fujimori, Fujimori, Shoichi, Yu Kawakami +9
Mathematics · #53A10 #53A35 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A10 #msc:53A35 #msc:53C50

paper · pdf · doi:10.48550/arxiv.1507.06695

12 pages, 8 figures

arxiv created 2018/07/09 · arxiv updated 2018/07/11

Abstract

Catenoids in de Sitter 3-space S³₁ belong to a certain class of space-like constant mean curvature one surfaces. In a previous work, the authors classified such catenoids, and found that two different classes of countably many exceptional elliptic catenoids are not realized as closed subsets in S³₁. Here we show that such exceptional catenoids have closed analytic extensions in S³₁ with interesting properties.

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