On the linear isoperimetric inequality
type: Item
instance of: scholarly article
title: On the linear isoperimetric inequality
zbMATH Open document ID: 0573.53004
DOI: 10.1007/BF01626400
author: Albrecht Küster
published in: Manuscripta Mathematica
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155099
review text: The author proves the following estimate for the area A(X) of a minimal surface X parametrized over the unit disc B in \({\mathbb{R}}^ 2: A(X)\leq R L(X| \partial B)\) where R is the radius of the smallest ball containing X(B) and L(X\(| \partial B)\) denotes the length of the boundary curve. This inequality being true for surfaces in \({\mathbb{R}}^ N\), the equality sign is only discussed for \(N=3:\) equality holds if and only if X is a plane disc of radius R. Two applications to minimal surfaces with free boundaries are given.
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 49Q05
zbMATH DE Number: 3915130
zbMATH Keywords: isoperimetric problem
zbMATH Keywords: area
zbMATH Keywords: minimal surface
reviewed by: F. Tomi
MaRDI profile type: Publication
cites work: Q3492251
cites work: Q5565773
cites work: An optimal estimate of the free boundary of a minima surface.
cites work: Q3344761
cites work: Q4081953
OpenAlex ID: W2323131542
description: scientific article; zbMATH DE number 3915130