Translating solutions to Lagrangian mean curvature flow

DOI10.1090/S0002-9947-2013-05649-8zbMath1282.53057arXiv0711.4341MaRDI QIDQ2849025

Tian, Gang, André Neves

Publication date: 16 September 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.4341

zbMATH Keywords

finite-time singularityLagrangian mean curvature flowspecial Lagrangiantranslating solution

Mathematics Subject Classification ID

Lagrangian submanifolds; Maslov index (53D12)

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Rigidity of self-shrinkers and translating solitons of mean curvature flows ⋮ Local non-collapsing of volume for the Lagrangian mean curvature flow ⋮ TRANSLATING SOLITONS FOR THE MEAN CURVATURE FLOW IN ⋮ Lagrangian mean curvature flow of Whitney spheres ⋮ Symplectic mean curvature flow in \(\mathbb CP^{2}\) ⋮ Rigidity of symplectic translating solitons ⋮ Uniqueness of Lagrangian self-expanders ⋮ Bernstein type theorems of translating solitons of the mean curvature flow in higher codimension ⋮ Finite time singularities for Lagrangian mean curvature flow ⋮ Mean curvature decay in symplectic and Lagrangian translating solitons ⋮ A uniqueness theorem of complete Lagrangian translator in \(\mathbb C^2\) ⋮ Ancient solutions in Lagrangian mean curvature flow ⋮ The second type singularities of symplectic and Lagrangian mean curvature flows ⋮ Lagrangian \(L\)-stability of Lagrangian translating solitons ⋮ Minimal cones and self-expanding solutions for mean curvature flows ⋮ Classification theorems of complete space-like Lagrangian \(\xi\)-surfaces in the pseudo-Euclidean space \(\mathbb{R}^4_2\) ⋮ Non-existence of eternal solutions to Lagrangian mean curvature flow with non-negative Ricci curvature ⋮ Rigidity of complete spacelike translating solitons in pseudo-Euclidean space ⋮ A Bernstein type result of translating solitons ⋮ Rigidity results on Lagrangian and symplectic translating solitons

Cites Work

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• Singularities of Lagrangian mean curvature flow: zero-Maslov class case
• Asymptotic behavior for singularities of the mean curvature flow
• Self-similar solutions and translating solitons for Lagrangian mean curvature flow
• Starshaped hypersurfaces and the mean curvature flow
• Elliptic regularization and partial regularity for motion by mean curvature
• The nature of singularities in mean curvature flow of mean-convex sets
• The size of the singular set in mean curvature flow of mean-convex sets

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