On the isoperimetric inequality on a minimal surface
type: Item
instance of: scholarly article
title: On the isoperimetric inequality on a minimal surface
zbMATH Open document ID: 1035.53019
author: Andrew Stone
published in: Calculus of Variations and Partial Differential Equations
publication date: 2003-09-01T00:00:00Z
review text: An explicit formula for the isoperimetric defect \(L^2-4\pi A\) of an arbitrary minimal surface \(\Sigma^2\subset\mathbb{R}^n\) of area \(A\), with smooth boundary \(\partial\Sigma\) of length \(L\), is derived -- in terms of a double surface integral of certain geometric quantities (Lemma 5.1). As a by-product the author shows that the best known universal isoperimetric estimate, that \(L^2\geq 2\pi A\) for any minimal surface \(\Sigma^2\subset\mathbb{R}^n\) (due to L. Simon), may be improved by the factor \(\sqrt 2\) to the universal estimate \(L^2\geq 2\pi A\sqrt 2\).
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 1973281
zbMATH Keywords: minimal surface
zbMATH Keywords: isoperimetric defect
zbMATH Keywords: universe isoperimetric estimate
MaRDI profile type: Publication
full work available at URL: s00526-002-0174-9
OpenAlex ID: W2001696300
DOI: 10.1007/S00526-002-0174-9
description: scientific article; zbMATH DE number 1973281