## 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.)

Hopf conjecture

Zbl 0699.53007
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