Surfaces of finite type with constant mean curvature
type: Item
instance of: scholarly article
title: Surfaces of finite type with constant mean curvature
zbMATH Open document ID: 0828.53006
author: Thomas Hasanis
author: T. Vlachos
published in: Kodai Mathematical Journal
publication date: 1996-01-14T00:00:00Z
review text: The authors prove the following results for finite type surfaces in the Euclidean 3-space \(E^3\). Theorem 1: A 3-type surface in \(E^3\) has nonconstant mean curvature. Theorem 2: Ordinary spheres, planes, catenoids and circular cylinders are the only surfaces of revolution with constant mean curvature in \(E^3\) which are of finite type.
reviewed by: Bang-Yen Chen
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 515596
zbMATH Keywords: surface of finite type
zbMATH Keywords: 2-type surface
zbMATH Keywords: 3-type surface
zbMATH Keywords: constant mean curvature
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039788
OpenAlex ID: W2170210781
cites work: Q3322795
cites work: Q3764820
cites work: Q3357833
cites work: Q4004704
cites work: A Property of Complete Minimal Surfaces
cites work: Spherical 2-type hypersurfaces
cites work: Compact constant mean curvature surfaces in Euclidean three-space
cites work: Critical point theory and submanifold geometry
cites work: Counterexample to a conjecture of H. Hopf
DOI: 10.2996/KMJ/1138039788
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description: scientific article; zbMATH DE number 515596