Constant mean curvature surfaces constructed by fusing Wente tori. (English) Zbl 0840.53005

This paper contains detailed proofs of the results announced in [the author, Proc. Natl. Acad. Sci. USA 89, No. 12, 5695-5698 (1992; Zbl 0763.53014)]. The main geometric result is the existence of infinitely many immersed \(C^\infty\) surfaces of constant mean curvature \(H = 1\) and genus \(g \geq 2\) into Euclidean 3-space. The main difficulties (as compared to the case of fusing Delaunay pieces) result from the different geometry of the flat point set. This requires completely new balancing concepts. The paper is conceptually difficult and technically extremely involved, as is emphasized by an index of more than fifty notational symbols given in the introduction.
Reviewer: D.Ferus (Berlin)


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


Zbl 0763.53014
Full Text: DOI EuDML


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