Minimal Surface Linear Combinatoin Theorem

2006/10/24 by Michael Dorff, Stephen Taylor, Dorff, Michael +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Analytic and geometric function theory #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0610706

openalex publication_date 2006/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given two univalent harmonic mappings f₁ and f₂ on \mathbbD, which lift to minimal surfaces via the Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for f₃=(1-s)f₁+sf₂ to lift to a minimal surface for s∈[0,1]. We then construct such mappings from Enneper's surface to Scherk's singularly periodic surface, Sckerk's doubly periodic surface to the catenoid, and the 4-Enneper surface to the 4-noid.

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