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

Abstract

Catenoids in de Sitter $3$-space $S_1^3$ 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 $S_1^3$. Here we show that such exceptional catenoids have closed analytic extensions in $S_1^3$ with interesting properties.

arXiv comment12 pages, 8 figures

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