A generalization of Steiner symmetrization for immersed surfaces and its applications
type: Item
instance of: scholarly article
title: A generalization of Steiner symmetrization for immersed surfaces and its applications
zbMATH Open document ID: 0838.53002
DOI: 10.1007/BF02570477
author: Miyuki Koiso
published in: Manuscripta Mathematica
publication date: 1996-06-04T00:00:00Z
full work available at URL: https://eudml.org/doc/156090
review text: The author generalizes the Steiner symmetrization to surfaces with self-intersections. Then he gives applications to the isoperimetric problem: consider an analytic Jordan curve \(C\) in a plane \(P\) of \(\mathbb{R}^3\), which is symmetric with respect to a plane \(P_1\) orthogonal to \(P\), and such that each plane orthogonal to \(P\) and \(P_1\) meets \(C\) in at most two points. If \(M\) is an immersed surface in one of the closed halfspaces determinated by \(P\) with boundary \(C\), which has smallest area among immersed surfaces bounded by \(C\) which enclose a given volume, then \(M\) is an embedding and is symmetric with respect to the plane \(P_1\).
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 784077
zbMATH Keywords: Steiner symmetrization
zbMATH Keywords: isoperimetric problem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 784077