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An unknotting result for complete minimal surfaces in \(\mathbb{R}^ 3\). (English) Zbl 0773.53003

The main theorem describes the closed connected complementary components of a complete properly embedded minimal surface in 3-space. They are either metrically \(\mathbb{R}^ 2\times[0,h]\) or, up to diffeomorphism, made from an at most countable collection of specified building blocks with a proper collection of handles attached. The proof uses the plane theorem of do Carmo, Peng and Fischer-Colbrie/Schoen and topological methods developed by Meeks, Yau and others.
Reviewer: D.Ferus (Berlin)

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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References:

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