On Chern's conjecture for minimal hypersurfaces and rigidity of self-shrinkers

DOI10.1016/j.jfa.2017.08.020zbMath1375.53058OpenAlexW2751878385MaRDI QIDQ2407215

Zhi-yuan Xu, Hong-Wei Xu

Publication date: 29 September 2017

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2017.08.020

zbMATH Keywords

second fundamental formrigidity theoremself-shrinkerChern conjecture for minimal hypersurfaces

Mathematics Subject Classification ID

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

Related Items (13)

The second gap on complete self-shrinkers ⋮ An optimal gap theorem for scalar curvature of CMC hypersurfaces in a sphere ⋮ A new gap for complete hypersurfaces with constant mean curvature in space forms ⋮ A note on the Chern conjecture in dimension four ⋮ A rigidity result of spacelike \(\xi \)-submanifolds in pseudo-Euclidean spaces ⋮ Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set ⋮ Complete self-similar hypersurfaces to the mean curvature flow with nonnegative constant scalar curvature ⋮ Complete hypersurfaces with 𝑤-constant mean curvature in the unit spheres ⋮ A new pinching theorem for complete self-shrinkers and its generalization ⋮ Ancient solutions to mean curvature flow for isoparametric submanifolds ⋮ On the generalized Chern conjecture for hypersurfaces with constant mean curvature in a sphere ⋮ 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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