New examples of minimal imbeddings of 𝑆^{{}𝑛-1} into 𝑆ⁿ(1)—The spherical Bernstein problem for 𝑛=4,5,6

DOI10.1090/S0273-0979-1982-15042-XzbMath0517.53057OpenAlexW1491517043MaRDI QIDQ3665853

Wu-yi Hsiang

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1090/s0273-0979-1982-15042-x

zbMATH Keywords

examplesminimal imbeddingminimal hyperspheresspherical hypersurfacesspherical Bernstein problem

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

• Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
• Minimal immersions of surfaces in Euclidean spheres
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• Minimal submanifolds of low cohomogeneity
• Examples of constant mean curvature immersions of the 3-sphere into euclidean 4-space
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