On semidiscrete constant mean curvature surfaces and their associated families
| Autor: | Wolfgang Carl |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
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 |
| Zdroj: | Monatshefte Fur Mathematik |
| ISSN: | 1436-5081 0026-9255 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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