Splitting of 3-manifolds and rigidity of area-minimising surfaces

DOI10.1090/S0002-9939-2015-12137-5zbMath1352.49043arXiv1107.5346MaRDI QIDQ5246912

Mario J. Micallef, Vlad Moraru

Publication date: 22 April 2015

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

Full work available at URL: https://arxiv.org/abs/1107.5346

zbMATH Keywords

3-manifoldsrigidityarea-minimizing surfaces

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Rigidity results (53C24) Inequalities involving derivatives and differential and integral operators (26D10)

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Cites Work

• Rigidity of area-minimizing hyperbolic surfaces in three-manifolds
• Rigidity of area-minimizing two-spheres in three-manifolds
• Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
• Rigidity of stable minimal hypersurfaces
• The inverse mean curvature flow and the Riemannian Penrose inequality
• Rigidity and positivity of mass for asymptotically hyperbolic manifolds
• Minimal varieties in Riemannian manifolds
• The splitting theorem for manifolds of nonnegative Ricci curvature
• A general comparison theorem with applications to volume estimates for submanifolds
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Some comments on gravitational entropy and the inverse mean curvature flow
• Rigidity of area minimizing tori in 3-manifolds of nonnegative scalar curvature
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