The global structure of constant mean curvature surfaces
type: Item
instance of: scholarly article
title: The global structure of constant mean curvature surfaces
zbMATH Open document ID: 0803.53040
DOI: 10.1007/BF01232673
author: Rob Kusner
author: Nicholas J. Korevaar
published in: Inventiones Mathematicae
publication date: 1994-12-18T00:00:00Z
full work available at URL: https://eudml.org/doc/144151
review text: Let MC1 denote a complete, finite topology, properly embedded surface with constant mean curvature 1. Kapouleas constructed a wealth of MC1 surfaces by starting with a linear graph in \(\mathbb{R}^ 3\) satisfying a balancing condition at each vertex. The present authors prove global properties of MC1 surfaces giving partial answers to a conjecture that all MC1 surfaces ``look like Kapouleas examples'' in some sense. In particular they use a force and torque vector assigned invariantly to each homology class of 1-cycles on an MC1 surface.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 549652
zbMATH Keywords: finite topology
zbMATH Keywords: constant mean curvature
zbMATH Keywords: Kapouleas examples
reviewed by: Konrad Polthier
MaRDI profile type: Publication
cites work: Complete constant mean curvature surfaces in Euclidean three-space
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cites work: On surfaces of constant mean curvature which span a given space curve
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description: scientific article; zbMATH DE number 549652