Isoperimetric inequalities for parametric variational problems
type: Item
instance of: scholarly article
title: Isoperimetric inequalities for parametric variational problems
zbMATH Open document ID: 1014.53009
DOI: 10.1016/S0294-1449(02)00096-3
author: Ulrich Clarenz
author: Heiko von der Mosel
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2002-09-17T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78556
review text: Isoperimectric inequalities for general parametric variational double integrals \({\mathcal F}\), whose Lagrangians \(F\) depend on the position vector \(X\) and the surface normal \(N\), are established. As an essential tool Sauvigny's \(F\)-conformal parameters adapted to the parametric integrand are introduced and use is made of the notion of generalised mean and Gaussian curvatures. The special cases of minimal surfaces, surfaces of bounded mean curvature and \({F}\)-minimising surfaces are also discussed.
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 49Q99
zbMATH DE Number: 1801803
zbMATH Keywords: minimal surfaces
zbMATH Keywords: critical immersions
zbMATH Keywords: isoperimetric inequality
reviewed by: Kaarin Riives
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1801803