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The structure of singly-periodic minimal surfaces. (English) Zbl 0695.53005
The authors generalize Riemann’s minimal surface by constructing an infinite family of properly embedded periodic minimal surfaces with an infinite number of (flat) ends. The symmetry is a group of translations, but the examples can be “twisted”, so that it becomes screw motion. Conversely it is shown that a properly embedded minimal surface with more than one end and infinite symmetry group either is a catenoid, or it has infinitely many ends, and is invariant under a screw motion.
Reviewer: D.Ferus

MSC:
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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