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arXiv · 0903.4194

Existence of proper minimal surfaces of arbitrary topological type

Leonor Ferrer·Francisco Martin·William H. Meeks III
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Abstract

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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Leonor Ferrer, Francisco Martin, William H. Meeks III. 2009-03-24. Existence of proper minimal surfaces of arbitrary topological type. https://arxiv.org/abs/0903.4194

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