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arXiv · 0910.4284

Complete minimal surfaces and harmonic functions

Antonio Alarcon·Isabel Fernandez·Francisco J. Lopez
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Abstract

We prove that for any open Riemann surface $M$ and any non constant harmonic function $h:M \to \mathbb{R},$ there exists a complete conformal minimal immersion $X:M \to \mathbb{R}^3$ whose third coordinate function coincides with $h.$ As a consequence, complete minimal surfaces with arbitrary conformal structure and whose Gauss map misses two points are constructed.

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Antonio Alarcon, Isabel Fernandez, Francisco J. Lopez. 2009-10-22. Complete minimal surfaces and harmonic functions. https://arxiv.org/abs/0910.4284

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