Constant mean curvature surfaces constructed by fusing Wente tori
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.
scientific article; zbMATH DE number 783996