On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces. I
type: Item
instance of: scholarly article
title: On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces. I
zbMATH Open document ID: 0682.53057
DOI: 10.1007/BF01388843
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143719
review text: In the case of constant curvature spaces \((E^ n,S^ n(1),H^ n(-1))\) one has the uniqueness of the solution to the isoperimetric problem, namely a round ball. On the other hand, by a theorem of A. D. Alexandrov, imbedded soap bubbles (i.e. closed constant mean curvature surfaces) in \(E^ n,S_+^ n\) or in \(H^ n\) are round spheres, hence congruent if they have same mean curvature. In this paper the authors replace the constant curvature spaces by a simply connected symmetric space with non- positive sectional curvature. They investigate generalizations of the two uniqueness theorems for the special case of products of hyperbolic (or Euclidean) spaces and prove a number of theorems in that direction.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 49Q05
zbMATH DE Number: 4117403
zbMATH Keywords: isoperimetric problem
zbMATH Keywords: soap bubbles
zbMATH Keywords: round spheres
zbMATH Keywords: symmetric space
author: Wu-teh Hsiang
author: Wu-Yi Hsiang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4117403