An isoperimetric comparison theorem for Schwarzschild space and other manifolds

DOI10.1090/S0002-9939-01-06186-XzbMath0994.53029MaRDI QIDQ2781307

Hubert L. Bray, Frank Morgan

Publication date: 19 March 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Schwarzschild spacetimeisoperimetric problemwarped product

Mathematics Subject Classification ID

Black holes (83C57) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

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Cites Work

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• Stable constant mean curvature tori and the isoperimetric problem in three space forms
• An isoperimetric comparison theorem
• Applications of compactness results for harmonic maps to stable constant mean curvature surfaces
• The inverse mean curvature flow and the Riemannian Penrose inequality
• Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces
• Proof of the Riemannian Penrose inequality using the positive mass theorem.
• The isoperimetric problem in spherical cylinders
• On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces. I
• The Isoperimetric Problem on Surfaces
• Isoperimetric regions in cones
• Unicity of constant mean curvature hypersurfaces in some riemannian manifolds
• The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature
• The spaces of index one minimal surfaces and stable constant mean curvature surfaces embedded in flat three manifolds
• Isoperimetric domains in the Riemannian product of a circle with a simply connected space form and applications to free boundary problems