Constant mean curvature surfaces constructed by fusing Wente tori
type: Item
instance of: scholarly article
title: Constant mean curvature surfaces constructed by fusing Wente tori
zbMATH Open document ID: 0840.53005
DOI: 10.1007/BF01245190
author: Nikolaos Kapouleas
published in: Inventiones Mathematicae
publication date: 1996-07-09T00:00:00Z
full work available at URL: https://eudml.org/doc/144263
review text: 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.
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 783996
zbMATH Keywords: unbalancing
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: linearized mean curvature equation
zbMATH Keywords: constant mean curvature surfaces
zbMATH Keywords: balancing
reviewed by: Dirk Ferus
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 783996