Existence of proper minimal surfaces of arbitrary topological type

Details Existence of proper minimal surfaces of arbitrary topological type Existence of proper minimal surfaces of arbitrary topological type

2009-03-24

arxiv.org/abs/0903.4194v1

Mathematics

Differential Geometry

33 pages, 10 figures

Scientific paper

Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f : M --> D. Moreover, if D is smooth and bounded, then we prove that the immersion f : M --> D can be chosen so that the limit sets of distinct ends of M are disjoint connected compact sets in the boundary of D.

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