Hamiltonian stationary self-similar solutions for Lagrangian mean curvature flow in the complex Euclidean plane

DOI10.1090/S0002-9939-09-10134-XzbMath1195.53091arXiv0906.3117MaRDI QIDQ3559013

Ildefonso Castro, Ana M. Lerma

Publication date: 11 May 2010

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

Full work available at URL: https://arxiv.org/abs/0906.3117

zbMATH Keywords

complex Euclidean planeLagrangian mean curvature flowHamiltonian stationary self-similar solution

Mathematics Subject Classification ID

Global submanifolds (53C40) Lagrangian submanifolds; Maslov index (53D12)

Related Items (18)

Mean Curvature Flow in Higher Codimension: Introduction and Survey ⋮ Hamiltonian F-stability of complete Lagrangian self-shrinkers ⋮ Rationally convex domains and singular Lagrangian surfaces in \(\mathbb {C}^2\) ⋮ Complete Lagrangian self-shrinkers in \(\mathbb{R}^4\) ⋮ Parabolicity, Brownian exit time and properness of solitons of the direct and inverse mean curvature flow ⋮ Uniqueness of Lagrangian self-expanders ⋮ A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves ⋮ Lagrangian F-stability of closed Lagrangian self-shrinkers ⋮ Complete Lagrangian self-expanders in \(\mathbb{C}^2\) ⋮ A uniqueness theorem of complete Lagrangian translator in \(\mathbb C^2\) ⋮ TRANSLATING SOLITONS FOR LAGRANGIAN MEAN CURVATURE FLOW IN COMPLEX EUCLIDEAN PLANE ⋮ Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space ⋮ New characterizations of the Clifford torus as a Lagrangian self-shrinker ⋮ Two non existence results for the self-similar equation in Euclidean 3-space ⋮ A rigidity theorem of \(\xi \)-submanifolds in \({\mathbb {C}}^{2}\) ⋮ Classification theorems of complete space-like Lagrangian \(\xi\)-surfaces in the pseudo-Euclidean space \(\mathbb{R}^4_2\) ⋮ Variational characterizations of \(\xi\)-submanifolds in the Eulicdean space \(\mathbb{R}^{m+p}\) ⋮ A characterization of the standard tori in \(\mathbb{C}^2\) as compact Lagrangian \(\xi \)-submanifolds

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