Global rigidity theorems for submanifolds with parallel mean curvature

DOI10.1007/s10473-023-0111-xOpenAlexW4306679368WikidataQ115235824 ScholiaQ115235824MaRDI QIDQ2088156

Pengfei Pan, En-Tao Zhao, Hong-Wei Xu

Publication date: 21 October 2022

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10473-023-0111-x

zbMATH Keywords

Euclidean spaceunit sphereglobal rigidity theoremsubmanifolds with parallel mean curvature

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Rigidity results (53C24)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric, topological and differentiable rigidity of submanifolds in space forms
• A new pinching theorem for closed hypersurfaces with constant mean curvature in \(S^{n+1}\)
• A new characterization of the Clifford torus via scalar curvature pinching
• On Chern's problem for rigidity of minimal hypersurfaces in the spheres
• Complete hypersurfaces with constant mean curvature and finite index in hyperbolic spaces
• On minimal hypersurfaces with constant scalar curvatures in \(S^ 4\)
• Geometric inequalities for certain submanifolds in a pinched Riemannian manifold
• Global pinching theorems for even dimensional minimal submanifolds in the unit spheres
• An intrinsic rigidity theorem for minimal submanifolds in a sphere
• A rigidity theorem for submanifolds with parallel mean curvature in a sphere
• An estimate of the pinching constant of minimal hypersurfaces with constant scalar curvature in the unit sphere
• Relative volume comparison with integral curvature bounds
• Chern's conjecture on minimal hypersurfaces
• The scalar curvature of minimal hypersurfaces in spheres
• Gap theorems for minimal submanifolds in \(\mathbb{R}^{n+1}\)
• \(L_{n/2}\)-pinching theorems for submanifolds with parallel mean curvature in a sphere
• New spectral characterizations of extremal hypersurfaces
• A general gap theorem for submanifolds with parallel mean curvature in \(\mathbb R^{n+p}\)
• The second pinching theorem for hypersurfaces with constant mean curvature in a sphere
• On Yau rigidity theorem for minimal submanifolds in spheres
• On Chern's conjecture for minimal hypersurfaces and rigidity of self-shrinkers
• Local rigidity theorems for minimal hypersurfaces
• Minimal varieties in Riemannian manifolds
• The pinching constant of minimal hypersurfaces in the unit spheres
• Hypersurfaces and a Pinching Problem on the Second Fundamental Tensor
• Submanifolds with Constant Mean Curvature
• Submanifolds with Constant Mean Curvature II
• A general rigidity theorem for complete submanifolds
• A Global Pinching Theorem of Minimal Hypersurfaces in the Sphere
• On Closed Minimal Submanifolds in Pinched Riemannian Manifolds
• THE SCALAR CURVATURE OF MINIMAL HYPERSURFACES IN A UNIT SPHERE
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
• Rigidity of minimal submanifolds in space forms
• Scalar curvature of minimal hypersurfaces in a sphere

This page was built for publication: Global rigidity theorems for submanifolds with parallel mean curvature