Complete minimal surfaces and harmonic functions
We prove that for any open Riemann surface N and any non-constant harmonic function hW
N! R, there exists a complete conformal minimal immersion XWN! 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.
N! R, there exists a complete conformal minimal immersion XWN! 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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