The rigidity theorems of self-shrinkers
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Publication:3190792
DOI10.1090/S0002-9947-2014-05901-1zbMath1316.53076arXiv1105.4962OpenAlexW2594399454MaRDI QIDQ3190792
Publication date: 19 September 2014
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1105.4962
Related Items (42)
Examples of compact \(\lambda\)-hypersurfaces in Euclidean spaces ⋮ The second gap on complete self-shrinkers ⋮ Submanifolds with parallel weighted mean curvature vector in the Gaussian space ⋮ Gap and rigidity theorems of 𝜆-hypersurfaces ⋮ The rigidity theorems of self shrinkers via Gauss maps ⋮ 2-dimensional complete self-shrinkers in \(\mathbb R^3\) ⋮ Complete Lagrangian self-shrinkers in \(\mathbb{R}^4\) ⋮ Vanishing theorems, higher order mean curvatures and index estimates for self-shrinkers ⋮ 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 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 ⋮ 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 ⋮ Classification of complete 3-dimensional self-shrinkers in the Euclidean space \(\mathbb{R}^4\) ⋮ Uniqueness of hypersurfaces in weighted product spaces via maximum principles for the drift Laplacian ⋮ A new pinching theorem for complete self-shrinkers and its generalization ⋮ SELF-SHRINKERS WITH SECOND FUNDAMENTAL FORM OF CONSTANT LENGTH ⋮ Some classifications of 2-dimensional self-shrinkers ⋮ Unnamed Item ⋮ A note on the characterization of spheres as self-shrinkers ⋮ A uniqueness theorem of complete Lagrangian translator in \(\mathbb C^2\) ⋮ Mean curvature flow solitons in the presence of conformal vector fields ⋮ Topics in differential geometry associated with position vector fields on Euclidean submanifolds ⋮ Complete \(\lambda \)-hypersurfaces of weighted volume-preserving mean curvature flow ⋮ Complete \(\lambda\)-surfaces in \(\mathbb{R}^3\) ⋮ New characterizations of the Clifford torus as a Lagrangian self-shrinker ⋮ Complete self-shrinkers of the mean curvature flow ⋮ 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 ⋮ Classification and rigidity of self-shrinkers in the mean curvature flow ⋮ Classification theorems of complete space-like Lagrangian \(\xi\)-surfaces in the pseudo-Euclidean space \(\mathbb{R}^4_2\) ⋮ Complete self-shrinkers with constant norm of the second fundamental form ⋮ Variational characterizations of \(\xi\)-submanifolds in the Eulicdean space \(\mathbb{R}^{m+p}\) ⋮ A gap theorem of self-shrinkers ⋮ Eigenvalues of the drifting Laplacian on smooth metric measure spaces ⋮ Complete \(\lambda\)-hypersurfaces in Euclidean spaces
Cites Work
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- Volume growth eigenvalue and compactness for self-shrinkers
- Generic mean curvature flow. I: Generic singularities
- Smooth compactness of self-shrinkers
- Blow-up rate of the mean curvature during the mean curvature flow and a gap theorem for self-shrinkers
- On Chern's problem for rigidity of minimal hypersurfaces in the spheres
- 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
- An intrinsic rigidity theorem for minimal submanifolds in a sphere
- Rigidity of compact minimal submanifolds in a unit sphere
- The scalar curvature of minimal hypersurfaces in spheres
- Gap theorems for minimal submanifolds in \(\mathbb{R}^{n+1}\)
- A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
- Mean curvature flow with convex Gauss image
- Local rigidity theorems for minimal hypersurfaces
- Minimal varieties in Riemannian manifolds
- Submanifolds with Constant Mean Curvature
- Logarithmic Sobolev inequalities on submanifolds of Euclidean space
- Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
- Sobolev and mean‐value inequalities on generalized submanifolds of Rn
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