On soap bubbles and isoperimetric regions in non-compact symmetric spaces. I

DOI10.2748/tmj/1178227334zbMath0819.53021OpenAlexW2037306585MaRDI QIDQ1312820

Wu-yi Hsiang

Publication date: 7 February 1994

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178227334

zbMATH Keywords

mean curvaturesoap bubblesisoparametric regionnon-compact symmetric spaces

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Differential geometry of symmetric spaces (53C35)

Related Items

The relative isoperimetric inequality in Cartan-Hadamard 3-manifolds ⋮ The relative isoperimetric inequality outside convex domains in \(\mathbb{R}^{n}\) ⋮ Constant mean curvature hypersurfaces in noncompact symmetric spaces ⋮ A modified mean curvature flow in Euclidean space and soap bubbles in symmetric spaces ⋮ The isoperimetric problem for lens spaces ⋮ A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\) ⋮ Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds ⋮ Isoperimetric inequalities in Euclidean convex bodies ⋮ The isoperimetric problem in complete surfaces of nonnegative curvature.

Cites Work

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• A characteristic property of spheres
• New examples of constant mean curvature immersions of (2k-1)-spheres into euclidean 2k-space
• Counterexample to a conjecture of H. Hopf
• Generalized rotational hypersurfaces of constant mean curvature in the Euclidean spaces. II
• Generalized rotational hypersurfaces of constant mean curvature in the euclidean spaces. I
• On the existence of codimension-one minimal spheres in compact symmetric spaces of rank 2. II
• Isoparametric submanifolds and their Coxeter groups
• The topology of isoparametric submanifolds
• On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces. I
• On the classification of constant mean curvature tori
• Minimal varieties in Riemannian manifolds
• Beweis der isoperimetrischen Eigenschaft der Kugel im hyperbolischen und sphärischen Raum jeder Dimensionszahl
• Constant mean curvature tori in terms of elliptic functions.
• Constant mean curvature surfaces in Euclidean three-space
• Examples of constant mean curvature immersions of the 3-sphere into euclidean 4-space
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• Über Flächen mit einer Relation zwischen den Hauptkrümmungen. Meinem Lehrer Erhard Schmidt in Verehrung und Freundschaft zum 75. Geburtstag gewidmet.

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