Some results on space-like self-shrinkers

DOI10.1007/s10114-014-4082-7zbMath1357.58021arXiv1211.2876OpenAlexW1984855728MaRDI QIDQ256408

Hua Qiao Liu, Yuan Long Xin

Publication date: 9 March 2016

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

Full work available at URL: https://arxiv.org/abs/1211.2876

zbMATH Keywords

rigidityvolume growthpseudo-distancespace-like self-shrinker

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Harmonic maps, etc. (58E20)

Related Items (12)

Rigidity of self-shrinkers and translating solitons of mean curvature flows ⋮ 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 ⋮ On the rigidity of spacelike submanifolds with parallel Gaussian mean curvature vector ⋮ A note on rigidity of spacelike self-shrinkers ⋮ Spacelike submanifolds with parallel Gaussian mean curvature vector: rigidity and nonexistence ⋮ Omori-Yau maximum principles, \(V\)-harmonic maps and their geometric applications ⋮ Rigidity theorems of spacelike entire self-shrinking graphs in the pseudo-Euclidean space ⋮ Singularities of mean curvature flow ⋮ A rigidity result of spacelike self-shrinkers in pseudo-Euclidean spaces ⋮ Classification theorems of complete space-like Lagrangian \(\xi\)-surfaces in the pseudo-Euclidean space \(\mathbb{R}^4_2\) ⋮ Rigidity of complete spacelike translating solitons in pseudo-Euclidean space

Cites Work

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• Volume growth eigenvalue and compactness for self-shrinkers
• Generic mean curvature flow. I: Generic singularities
• On the entire self-shrinking solutions to Lagrangian mean curvature flow
• Mean curvature flow with bounded Gauss image
• Comparison geometry for the Bakry-Emery Ricci tensor
• On the Gauss image of a spacelike hypersurface with constant mean curvature in Minkowski space
• Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
• Interior estimates and longtime solutions for mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space
• Mean curvature flow of spacelike hypersurfaces near null initial data
• The rigidity theorems for Lagrangian self-shrinkers
• Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes
• Rigidity of entire self-shrinking solutions to curvature flows
• Volume estimate about shrinkers
• Euclidean 𝑛-planes in pseudo-euclidean spaces and differential geometry of Cartan domains
• Some aspects of the global geometry of entire space-like submanifolds

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