A Global Pinching Theorem of Minimal Hypersurfaces in the Sphere

DOI10.2307/2046755zbMath0679.53049OpenAlexW3139996343MaRDI QIDQ4728958

Chun-li Shen

Publication date: 1989

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

Full work available at URL: https://doi.org/10.2307/2046755

zbMATH Keywords

sphereminimal hypersurfacetotally geodesiclength of the second fundamental form

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (13)

An application of Moser iteration to complete minimal submanifolds in a sphere ⋮ Characterizations of complete spacelike submanifolds in the \((n+p)\)-dimensional anti-de Sitter space of index \(q\) ⋮ Characterizing small spheres in a unit sphere by Fischer-Marsden equation ⋮ On energy gap phenomena of the Whitney spheres in \(\mathbb{C}^n\) or \(\mathbb{CP}^n\) ⋮ Some rigidity results of minimal submanifolds in space forms ⋮ Geometric and topological rigidity for compact submanifolds of odd dimension ⋮ A gap theorem for complete submanifolds with parallel mean curvature in the hyperbolic space ⋮ \(L^2\)-isolation phenomenon for complete surfaces arising from Yang-Mills theory ⋮ A global pinching theorem for compact surfaces inS 3 with constant mean curvature ⋮ A global pinching theorem for surfaces with constant mean curvature in $S^3$ ⋮ Rigidity of minimal submanifolds in space forms ⋮ A lower bound for 𝐿₂ length of second fundamental form on minimal hypersurfaces ⋮ Global rigidity theorems for submanifolds with parallel mean curvature

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