Minimal reflection surfaces in \mathbb S³. Combinatorics of curvature lines and minimal surfaces based on fundamental pentagons

2024/06/18 by Alexander I. Bobenko, Bobenko, Alexander I., Sebastian Heller +3 · 1 citation
Computer Science · #53A10 #53C42 #53C43 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #Digital Image Processing Techniques #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2406.12183

openalex publication_date 2024/06/18 · openalex created_date 2024/06/20 · openalex updated_date 2026/07/28

Abstract

We study compact minimal surfaces in the 3-sphere which are constructed by successive reflections from a minimal n-gon -- so-called minimal reflection surfaces. The minimal n-gon solves a free boundary problem in a fundamental piece of the respective reflection group. We investigate the combinatorics of the curvature lines of reflection surfaces, and construct new examples of minimal reflection surfaces based on pentagons. We end the paper by discussing the area of these minimal surfaces.

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• Application of Chern-Simons gauge theory to the enclosed volume of constant mean curvature surfaces in the 3-sphere

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