Every three-sphere of positive Ricci curvature contains a minimal embedded torus

DOI10.1090/S0273-0979-1989-15765-0zbMath0689.53003WikidataQ125747057 ScholiaQ125747057MaRDI QIDQ3031547

Brian White

Publication date: 1989

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

zbMATH Keywords

mapping degreecritical manifoldminimal embedded surfaces

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items (2)

Degree Theory of Immersed Hypersurfaces ⋮ Asymptotically flat three-manifolds contain minimal planes

Cites Work

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• The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
• New applications of mapping degrees to minimal surface theory
• Extreme curves bound embedded minimal surfaces of the type of the disc
• Embedded minimal surfaces in manifolds diffeomorphic to the three-dimensional ball or sphere
• Three-manifolds with positive Ricci curvature
• Complete minimal surfaces in \(S^ 3\)
• Equivariant minimax and minimal surfaces in geometric three-manifolds

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