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Minimal surfaces with genus zero. (English) Zbl 1243.49047

Iglesias Ponte, David (ed.) et al., Proceedings of the XV international workshop on geometry and physics, Puerto de la Cruz, Spain, September 11–16, 2006. Madrid: Real Sociedad Matemática Española (ISBN 978-84-935196-1-2/pbk). Publicaciones de la Real Sociedad Matemática Española 11, 337-342 (2007).
Summary: A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known classification results for properly embedded minimal surfaces with genus zero in \(\mathbb{R}^3\) or quotients of \(\mathbb{R}^3\) by one or two independent translations.
For the entire collection see [Zbl 1216.00039].

MSC:

49Q05 Minimal surfaces and optimization
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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