Lower volume growth estimates for self-shrinkers of mean curvature flow

DOI10.1090/S0002-9939-2014-12037-5zbMath1298.53064arXiv1112.0828OpenAlexW2021251630MaRDI QIDQ3190212

Yong Wei, Haizhong Li

Publication date: 16 September 2014

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

Full work available at URL: https://arxiv.org/abs/1112.0828

zbMATH Keywords

mean curvature flowself-shrinkervolume growth estimate

Mathematics Subject Classification ID

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

Related Items (12)

Diameter estimation of gradient \(\rho \)-Einstein solitons ⋮ On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking solitons ⋮ Complete space-like \(\lambda \)-surfaces in the Minkowski space \(\mathbb{R}_1^3\) with the second fundamental form of constant length ⋮ Classification of complete 3-dimensional self-shrinkers in the Euclidean space \(\mathbb{R}^4\) ⋮ Minimal submanifolds in a metric measure space ⋮ Complete \(\lambda\)-surfaces in \(\mathbb{R}^3\) ⋮ Remark on a lower diameter bound for compact shrinking Ricci solitons ⋮ A rigidity theorem on the second fundamental form for self-shrinkers ⋮ Classification and rigidity of self-shrinkers in the mean curvature flow ⋮ Critical Points of the Weighted Area Functional ⋮ Complete self-shrinkers with constant norm of the second fundamental form ⋮ Complete \(\lambda\)-hypersurfaces in Euclidean spaces

Cites Work

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• Asymptotic behavior for singularities of the mean curvature flow
• Sharp logarithmic Sobolev inequalities on gradient solitons and applications
• A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
• A Bernstein type theorem for self-similar shrinkers
• Logarithmic Sobolev inequalities on submanifolds of Euclidean space
• Geometry of Complete Gradient Shrinking Ricci Solitons
• Volume estimate about shrinkers
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ

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