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The classification of singly periodic minimal surfaces with genus zero and Scherk-type ends. (English) Zbl 1110.53008
Let us consider the space \(S(k)\) of complete embedded singly periodic minimal surfaces in Euclidean 3-space which in the quotient have genus zero and \(2k\) Scherk-type ends. Many things are already known about \(S(2)\). Authors prove a very interesting result about \(S(k)\) with \(k\) greater than or equal to 3, in terms of a 1-1 correspondence between this space and a certain space of convex unitary nonspecial polygons. An excellent and original research paper.

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