An estimate of the pinching constant of minimal hypersurfaces with constant scalar curvature in the unit sphere

DOI10.1007/BF02567445zbMath0934.53039MaRDI QIDQ1340224

Qing-Ming Cheng, Hongcang Yang

Publication date: 10 April 2000

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155980

zbMATH Keywords

minimal surfaceconstant scalar curvature

Mathematics Subject Classification ID

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

Related Items (15)

THE SCALAR CURVATURE OF MINIMAL HYPERSURFACES IN A UNIT SPHERE ⋮ An optimal gap theorem for scalar curvature of CMC hypersurfaces in a sphere ⋮ Unnamed Item ⋮ A new gap for complete hypersurfaces with constant mean curvature in space forms ⋮ On Chern's conjecture for minimal hypersurfaces and rigidity of self-shrinkers ⋮ Characterizing small spheres in a unit sphere by Fischer-Marsden equation ⋮ Complete hypersurfaces with 𝑤-constant mean curvature in the unit spheres ⋮ On the second pinching theorem for Willmore hypersurfaces in a sphere ⋮ Rigidity of complete minimal submanifolds in a hyperbolic space ⋮ Minimal hypersurfaces in nearly \(G_2\) manifolds ⋮ Minimal hypersurfaces in a nearly Kaehler 6-sphere ⋮ On the generalized Chern conjecture for hypersurfaces with constant mean curvature in a sphere ⋮ CONSTANT MEAN CURVATURE HYPERSURFACES IN SPHERES ⋮ Global rigidity theorems for submanifolds with parallel mean curvature ⋮ Closed Willmore minimal hypersurfaces with constant scalar curvature in \(\mathbb{S}^5(1)\) are isoparametric

Cites Work

• A note on the pinching constant of minimal hypersurfaces with constant scalar curvature in the unit sphere
• Local rigidity theorems for minimal hypersurfaces
• Minimal varieties in Riemannian manifolds
• Submanifolds with Constant Mean Curvature II

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