2-dimensional complete self-shrinkers in \(\mathbb R^3\)

DOI10.1007/S00209-016-1665-2zbMath1354.53074arXiv1504.02225OpenAlexW1614786242MaRDI QIDQ330005

Qing-Ming Cheng, Shiho Ogata

Publication date: 24 October 2016

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.02225

zbMATH Keywords

mean curvature flowgeneralized maximum principlecomplete self-shrinkers

Mathematics Subject Classification ID

Global submanifolds (53C40)

Related Items (20)

The second gap on complete self-shrinkers ⋮ Submanifolds with parallel weighted mean curvature vector in the Gaussian space ⋮ On the complete 2-dimensional \(\lambda\)-translators with a second fundamental form of constant length ⋮ Complete Lagrangian self-shrinkers in \(\mathbb{R}^4\) ⋮ Complete space-like \(\lambda \)-surfaces in the Minkowski space \(\mathbb{R}_1^3\) with the second fundamental form of constant length ⋮ Complete self-similar hypersurfaces to the mean curvature flow with nonnegative constant scalar curvature ⋮ Rigidity and gap results for the Morse index of self-shrinkers with any codimension ⋮ Complete 3-dimensional \(\lambda \)-translators in the Minkowski space \(\mathbb{R}^4_1 \) ⋮ Classification of complete 3-dimensional self-shrinkers in the Euclidean space \(\mathbb{R}^4\) ⋮ Aspects of mean curvature flow solitons in warped products ⋮ Lower order eigenvalues of a system of equations of the drifting Laplacian on the metric measure spaces ⋮ Some classifications of 2-dimensional self-shrinkers ⋮ Unnamed Item ⋮ Complete \(\lambda\)-surfaces in \(\mathbb{R}^3\) ⋮ Rigidity of self-shrinkers with constant squared norm of the second fundamental form ⋮ Complete \(3\)-dimensional \(\lambda \)-translators in the Euclidean space \(\mathbb{R}^4\) ⋮ A rigidity theorem on the second fundamental form for self-shrinkers ⋮ Singularities of mean curvature flow ⋮ Complete self-shrinkers with constant norm of the second fundamental form ⋮ Complete \(\lambda\)-hypersurfaces in Euclidean spaces

Cites Work

• Unnamed Item
• Volume growth eigenvalue and compactness for self-shrinkers
• Generic mean curvature flow. I: Generic singularities
• 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
• A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
• Complete self-shrinkers of the mean curvature flow
• Local rigidity theorems for minimal hypersurfaces
• Self-similar solutions to the curve shortening flow
• The rigidity theorems of self-shrinkers
• Volume estimate about shrinkers
• A gap theorem of self-shrinkers

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