The rigidity theorems of self shrinkers via Gauss maps

DOI10.1016/j.aim.2016.08.019zbMath1356.53065arXiv1203.1096OpenAlexW2963195283MaRDI QIDQ323663

Ling Yang, Qi Ding, Yuan Long Xin

Publication date: 10 October 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.1096

zbMATH Keywords

Gauss mapGrassmannian manifoldsconvex geometryself-shrinkers

Mathematics Subject Classification ID

Related Items (19)

Rigidity of self-shrinkers and translating solitons of mean curvature flows ⋮ Rigidity results for self-shrinking surfaces in \(\mathbb{R}^4\) ⋮ A Bernstein type theorem for entire graphic 2-dimensional \(\Lambda \)-submanifolds in \(\mathbf{R}^4 \) ⋮ Gauss maps of translating solitons of mean curvature flow ⋮ A rigidity result of spacelike \(\xi \)-submanifolds in pseudo-Euclidean spaces ⋮ Remarks on mean curvature flow solitons in warped products ⋮ Rigidity of mean curvature flow solitons and uniqueness of solutions of the mean curvature flow soliton equation in certain warped products ⋮ Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set ⋮ On the rigidity of mean curvature flow solitons in certain semi-Riemannian warped products ⋮ Aspects of mean curvature flow solitons in warped products ⋮ Omori-Yau maximum principles, \(V\)-harmonic maps and their geometric applications ⋮ A pointwise approach to rigidity of almost graphical self-shrinking solutions of mean curvature flows ⋮ Geometric properties of self-shrinkers in cylinder shrinking Ricci solitons ⋮ A rigidity theorem on the second fundamental form for self-shrinkers ⋮ Singularities of mean curvature flow ⋮ Submanifolds with parallel Gaussian mean curvature vector in Euclidean spaces ⋮ Bernstein-type theorem of translating solitons in arbitrary codimension with flat normal bundle ⋮ A Bernstein type theorem for minimal hypersurfaces via Gauss maps ⋮ Rigidity of complete spacelike translating solitons in pseudo-Euclidean space

Cites Work

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• On the Gauss map of complete surfaces of constant mean curvature in \(R^ 3 \)and \(R^ 4\).
• Harmonic maps to spheres
• Heat flow of equivariant harmonic maps from \(\mathbb{B}^ 3\) into \(\mathbb{C}\mathbb{P}^ 2\)
• A Bernstein type theorem for self-similar shrinkers
• The rigidity theorems for Lagrangian self-shrinkers
• Rigidity of entire self-shrinking solutions to curvature flows
• The rigidity theorems of self-shrinkers
• Volume estimate about shrinkers
• The Tension Field of the Gauss Map
• Convex Functions and Harmonic Maps

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