A gap theorem of self-shrinkers

DOI10.1090/S0002-9947-2015-06161-3zbMath1314.53118arXiv1212.6028MaRDI QIDQ5247022

Guoxin Wei, Qing-Ming Cheng

Publication date: 22 April 2015

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

Full work available at URL: https://arxiv.org/abs/1212.6028

zbMATH Keywords

second fundamental formelliptic operatorself-shrinkers

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (22)

Examples of compact \(\lambda\)-hypersurfaces in Euclidean spaces ⋮ The second gap on complete self-shrinkers ⋮ 2-dimensional complete self-shrinkers in \(\mathbb R^3\) ⋮ Complete Lagrangian self-shrinkers in \(\mathbb{R}^4\) ⋮ Gap theorems for complete \(\lambda\)-hypersurfaces ⋮ Self-shrinker type submanifolds in the Euclidean space ⋮ On Chern's conjecture for minimal hypersurfaces and rigidity of self-shrinkers ⋮ A rigidity result of spacelike \(\xi \)-submanifolds in pseudo-Euclidean spaces ⋮ Complete space-like \(\lambda \)-surfaces in the Minkowski space \(\mathbb{R}_1^3\) with the second fundamental form of constant length ⋮ 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 ⋮ Classification of complete 3-dimensional self-shrinkers in the Euclidean space \(\mathbb{R}^4\) ⋮ A new pinching theorem for complete self-shrinkers and its generalization ⋮ Topics in differential geometry associated with position vector fields on Euclidean submanifolds ⋮ Complete \(\lambda\)-surfaces in \(\mathbb{R}^3\) ⋮ New characterizations of the Clifford torus as a Lagrangian self-shrinker ⋮ A rigidity theorem on the second fundamental form for self-shrinkers ⋮ Singularities of mean curvature flow ⋮ A note on rigidity theorem of λ-hypersurfaces ⋮ Submanifolds with parallel Gaussian mean curvature vector in Euclidean spaces ⋮ Complete self-shrinkers with constant norm of the second fundamental form ⋮ Complete \(\lambda\)-hypersurfaces in Euclidean spaces

Cites Work

• Volume growth eigenvalue and compactness for self-shrinkers
• Generic mean curvature flow. I: Generic singularities
• Blow-up rate of the mean curvature during the mean curvature flow and a gap theorem for self-shrinkers
• Classification and rigidity of self-shrinkers in the mean curvature flow
• Flow by mean curvature of convex surfaces into spheres
• Asymptotic behavior for singularities of the mean curvature flow
• The normalized curve shortening flow and homothetic solutions
• Chern's conjecture on minimal hypersurfaces
• A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
• The rigidity theorems of self-shrinkers
• Unnamed Item
• Unnamed Item

This page was built for publication: A gap theorem of self-shrinkers