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Compact constant mean curvature surfaces in Euclidean three-space. (English) Zbl 0727.53063
The author extends the method of his earlier paper [Ann. Math., II. Ser. 131, 239-330 (1990; Zbl 0699.53007)]. He shows the existence of closed constant mean curvature surfaces of any genus \(>2\) with certain symmetries, and of many such without symmetry. He also obtains complete constant mean curvature surfaces of any genus \(>2\) with boundary a planar round circle.
Reviewer: D.Ferus (Berlin)

MSC:
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
Keywords:
Hopf conjecture
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