Minimal Surfaces from Rigid Motions

2020/09/10 by Jens Hoppe, Hoppe, Jens
Mathematics · #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.2009.05031

openalex publication_date 2020/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Equations are derived for the shape of a hypersurface in ℝ^N for which a rigid motion yields a minimal surface in ℝ^N+1. Some elementary, but unconventional, aspects of the classical case N=2 (solved by H.F. Scherk in 1835) are discussed in some detail.

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