A characterization of rotational minimal surfaces in the de Sitter space

2022/08/29 by Rafael López, López, Rafael
Mathematics · #53C40 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2208.13698

openalex publication_date 2022/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The generating curves of rotational minimal surfaces in the de Sitter space \s₁³ are characterized as solutions of a variational problem. It is proved that these curves are the critical points of the center of mass among all curves of \s₁² with prescribed endpoints and fixed length. This extends the known properties of the catenary and the catenoid in the Euclidean setting.

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