Minimal Surface Linear Combinatoin Theorem

Details Minimal Surface Linear Combinatoin Theorem Minimal Surface Linear Combinatoin Theorem

2006-10-24

arxiv.org/abs/math/0610706v1

Mathematics

Differential Geometry

Scientific paper

Given two univalent harmonic mappings $f_1$ and $f_2$ on $\mathbb{D}$, which lift to minimal surfaces via the Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for $f_3=(1-s)f_1+sf_2$ to lift to a minimal surface for $s\in[0,1]$. 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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