New complete embedded minimal surfaces in H2xR

2009/11/30 by Juncheol Pyo, Pyo, Juncheol
Computer Science · Engineering · Mathematics · #53A35 #53C40 #53C42 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.0911.5577

openalex publication_date 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct three kinds of complete embedded minimal surfaces in \Bbb H²× \Bbb R. The first is a simply connected, singly periodic, infinite total curvature surface. The second is an annular finite total curvature surface. These two are conjugate surfaces just as the helicoid and the catenoid are in \mathbb R³. The third one is a finite total curvature surface which is conformal to \mathbb S²∖\p₁,...,p_k\, k≥3.

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