On the numerical approximation and computation of minimal surface continua bounded by one-parameter families of polygonal contours
type: Item
instance of: scholarly article
title: On the numerical approximation and computation of minimal surface continua bounded by one-parameter families of polygonal contours
zbMATH Open document ID: 0883.65057
DOI: 10.1016/S0168-9274(97)00045-7
author: M. Hinze
published in: Applied Numerical Mathematics
publication date: 1998-03-29T00:00:00Z
review text: A mapping \(u\in C^0(\overline B,\mathbb{R}^q)\cap C^2(B,\mathbb{R}^q)\) is called a disc-type minimal surface spanning \(\Gamma\) (Jordan curve in \(\mathbb{R}^q\)) if \(u\) satisfies \(\Delta u= 0\) and \(|u_{x_1}|^2-|u_{x_2}|^2= 0\) in \(B\), \(u|_{\partial B}\) is a (weakly) monotone parameterization of \(\Gamma\). For arbitrary, but fixed polygons \(\Gamma\) the corresponding Shiffman's function was studied numerically by the author [Numer. Math. 73, No. 1, 95-118 (1996; Zbl 0858.65060)]. In the present paper, these results are extended to classes of polygons \(\Gamma=\Gamma(\alpha)\), where \(\alpha\) varies in certain subsets of finite-dimensional spaces.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 49Q05
zbMATH DE Number: 1072315
zbMATH Keywords: polygonal contours
zbMATH Keywords: minimal surface
reviewed by: Hans Benker
describes a project that uses: ALCON
describes a project that uses: Surface Evolver
MaRDI profile type: Publication
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full work available at URL: s0168-9274(97)00045-7
OpenAlex ID: W2084108269
description: scientific article; zbMATH DE number 1072315