Complete space-like \(\lambda \)-surfaces in the Minkowski space \(\mathbb{R}_1^3\) with the second fundamental form of constant length

DOI10.1007/S10114-020-9078-XzbMath1440.53110OpenAlexW3017897592MaRDI QIDQ2184634

Yangyang Liu, Ruina Qiao, Xing Xiao Li

Publication date: 29 May 2020

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-020-9078-x

zbMATH Keywords

second fundamental formmean curvatureself-shrinkersspace-like \(\lambda \)-surfaces

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Flows related to mean curvature (53E10)

Related Items (1)

A rigidity result of spacelike \(\xi \)-submanifolds in pseudo-Euclidean spaces

Cites Work

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• Some results on space-like self-shrinkers
• Rigidity of self-shrinkers and translating solitons of mean curvature flows
• 2-dimensional complete self-shrinkers in \(\mathbb R^3\)
• 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
• Omori-Yau maximum principles, \(V\)-harmonic maps and their geometric applications
• Rigidity theorems of \(\lambda\)-hypersurfaces
• On the entire self-shrinking solutions to Lagrangian mean curvature flow
• Classification and rigidity of self-shrinkers in the mean curvature flow
• The hyperplane is the only stable, smooth solution to the isoperimetric problem in Gaussian space
• Spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-Euclidean spaces
• Asymptotic behavior for singularities of the mean curvature flow
• The normalized curve shortening flow and homothetic solutions
• Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
• Complete bounded \(\lambda\)-hypersurfaces in the weighted volume-preserving mean curvature flow
• Complete \(\lambda \)-hypersurfaces of weighted volume-preserving mean curvature flow
• A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
• New characterizations of the Clifford torus as a Lagrangian self-shrinker
• Complete self-shrinkers of the mean curvature flow
• Complete Lagrangian self-shrinkers in \(\mathbb{R}^4\)
• A new pinching theorem for complete self-shrinkers and its generalization
• On the existence of a closed, embedded, rotational \(\lambda \)-hypersurface
• Gap theorems for complete \(\lambda\)-hypersurfaces
• The rigidity theorems for Lagrangian self-shrinkers
• A rigidity theorem of \(\xi \)-submanifolds in \({\mathbb {C}}^{2}\)
• Local rigidity theorems for minimal hypersurfaces
• Stability and area growth of \(\lambda\)-hypersurfaces
• Self-similar solutions to the curve shortening flow
• Rigidity of entire self-shrinking solutions to curvature flows
• Gap and rigidity theorems of 𝜆-hypersurfaces
• Lower volume growth estimates for self-shrinkers of mean curvature flow
• The rigidity theorems of self-shrinkers
• Numerical analysis of two local conservative methods for two-dimensional nonlinear Schrödinger equation
• A note on rigidity theorem of λ-hypersurfaces
• A gap theorem of self-shrinkers
• Some aspects of the global geometry of entire space-like submanifolds

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