Hyperbolic complete minimal surfaces with arbitrary topology

López, F.

doi:10.1090/S0002-9947-98-01932-1

Hyperbolic complete minimal surfaces with arbitrary topology
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by F. J. López PDF

Trans. Amer. Math. Soc. 350 (1998), 1977-1990 Request permission

Abstract:

We show a method to construct orientable minimal surfaces in $\mathbb {R}^3$ with arbitrary topology. This procedure gives complete examples of two different kinds: surfaces whose Gauss map omits four points of the sphere and surfaces with a bounded coordinate function. We also apply these ideas to construct stable minimal surfaces with high topology which are incomplete or complete with boundary.

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