The gap phenomenon for extremal submanifolds in a sphere

DOI10.1016/j.difgeo.2010.11.001zbMath1216.53056OpenAlexW1987635900WikidataQ115357045 ScholiaQ115357045MaRDI QIDQ531713

Dengyun Yang, Hong-Wei Xu

Publication date: 19 April 2011

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2010.11.001

zbMATH Keywords

mean curvatureflat normal bundleSobolev inequalitytotally umbilical surfaceextremal functional

Mathematics Subject Classification ID

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

Related Items

Characterization of Whitney spheres among Lagrangian submanifolds with conformal Maslov form ⋮ Rigidity of Willmore submanifolds and extremal submanifolds in the unit sphere ⋮ On the compactness of hypersurfaces with finite total curvature via mean curvature flow ⋮ A new characterization of Willmore submanifolds ⋮ Rigidity of minimal submanifolds in space forms

Cites Work

• An intrinsic rigidity theorem for minimal submanifolds in a sphere
• Willmore submanifolds in a sphere.
• \(L_{n/2}\)-pinching theorems for submanifolds with parallel mean curvature in a sphere
• A variational problem for submanifolds in a sphere
• Curvature and rigidity of Willmore submanifolds
• Local rigidity theorems for minimal hypersurfaces
• Minimal varieties in Riemannian manifolds
• Some remarks on minimal submanifolds
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length