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On semidiscrete constant mean curvature surfaces and their associated families
- Source :
- Monatshefte Fur Mathematik
- Publication Year :
- 2016
- Publisher :
- Springer Vienna, 2016.
-
Abstract
- The present paper studies semidiscrete surfaces in three-dimensional Euclidean space within the framework of integrable systems. In particular, we investigate semidiscrete surfaces with constant mean curvature along with their associated families. The notion of mean curvature introduced in this paper is motivated by a recently developed curvature theory for quadrilateral meshes equipped with unit normal vectors at the vertices, and extends previous work on semidiscrete surfaces. In the situation of vanishing mean curvature, the associated families are defined via a Weierstrass representation. For the general cmc case, we introduce a Lax pair representation that directly defines associated families of cmc surfaces, and is connected to a semidiscrete \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sinh $$\end{document}sinh-Gordon equation. Utilizing this theory we investigate semidiscrete Delaunay surfaces and their connection to elliptic billiards.
- Subjects :
- Mathematics(all)
39A12
General Mathematics
02 engineering and technology
Curvature
01 natural sciences
Constant mean curvature
Article
53A05
Mathematics::Numerical Analysis
Lax pair representation
0202 electrical engineering, electronic engineering, information engineering
0101 mathematics
Mathematics
Mean curvature
Delaunay triangulation
Euclidean space
010102 general mathematics
Mathematical analysis
Hyperbolic function
53A10
020207 software engineering
Associated family
Connection (mathematics)
Semidiscrete surface
Lax pair
Mathematics::Differential Geometry
Constant (mathematics)
Weierstrass representation
Subjects
Details
- Language :
- English
- ISSN :
- 14365081 and 00269255
- Volume :
- 182
- Issue :
- 3
- Database :
- OpenAIRE
- Journal :
- Monatshefte Fur Mathematik
- Accession number :
- edsair.doi.dedup.....c04d9f5c4e2e22974364a7b56e4232e2