Hamiltonian stationary cones and self-similar solutions in higher dimension

DOI10.1090/S0002-9947-09-04795-3zbMath1189.53066arXiv0802.0359OpenAlexW2152588682MaRDI QIDQ3550544

Yng-Ing Lee, Mu-Tao Wang

Publication date: 31 March 2010

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

Full work available at URL: https://arxiv.org/abs/0802.0359

zbMATH Keywords

self-shrinkerLagrangian mean curvature flowHamiltonian stationaryself-expanderBrakke floweternal solution

Mathematics Subject Classification ID

Lagrangian submanifolds; Maslov index (53D12) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (13)

Hamiltonian F-stability of complete Lagrangian self-shrinkers ⋮ Codimension bounds and rigidity of ancient mean curvature flows by the tangent flow at −∞ ⋮ Complete Lagrangian self-shrinkers in \(\mathbb{R}^4\) ⋮ Uniqueness of Lagrangian self-expanders ⋮ Some examples of self-similar solutions and translating solitons for Lagrangian mean curvature flow ⋮ Lagrangian F-stability of closed Lagrangian self-shrinkers ⋮ Uniqueness of asymptotically conical higher codimension self-shrinkers and self-expanders ⋮ Complete Lagrangian self-expanders in \(\mathbb{C}^2\) ⋮ Lagrangian mean curvature flows and moment maps ⋮ TRANSLATING SOLITONS FOR LAGRANGIAN MEAN CURVATURE FLOW IN COMPLEX EUCLIDEAN PLANE ⋮ Hamiltonian stationary self-similar solutions for Lagrangian mean curvature flow in the complex Euclidean plane ⋮ New characterizations of the Clifford torus as a Lagrangian self-shrinker ⋮ The stability of self-shrinkers of mean curvature flow in higher co-dimension

Cites Work

• Asymptotic behavior for singularities of the mean curvature flow
• Self-similar solutions and translating solitons for Lagrangian mean curvature flow
• Hamiltonian stationary shrinkers and expanders for Lagrangian mean curvature flows
• Calibrated geometries
• Deforming area preserving diffeomorphism of surfaces by mean curvature flow.
• Long-time existence and convergence of graphic mean curvature flow in arbitrary codimension.
• Minimizing area among Lagrangian surfaces: the mapping problem.
• Mean curvature flows of Lagrangians submanifolds with convex potentials.
• Angle theorems for the Lagrangian mean curvature flow
• Special Lagrangian \(m\)-folds in \(\mathbb{C}^m\) with symmetries
• The geometric complexity of special Lagrangian \(T^2\)-cones
• Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons
• Mirror symmetry is \(T\)-duality
• Lagrangian homology classes without regular minimizers
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Special Lagrangian cones
• Constructing special Lagrangian \(m\)-folds in \(\mathbb{C}^m\) by evolving quadrics

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