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Mean curvature flow of Lagrangian submanifolds with isolated conical singularities
Lagrangian submanifolds isolated conical singularities Differential Geometry
2011/9/20
Abstract: In this paper we study the short time existence problem for the (generalized) Lagrangian mean curvature flow in (almost) Calabi--Yau manifolds when the initial Lagrangian submanifold has iso...
Minimal Lagrangian submanifolds in indefinite complex space
Lagrangian submanifolds complex space
2010/11/22
Consider the complex linear space C^n endowed with the natural pseudo-Hermitian form <<.,.>>_p of signature p. This yields both a pseudo-Riemannian and a symplectic structure on C^n. We prove that th...
Construction of homogeneous Lagrangian submanifolds in $\CP^n$ and Hamiltonian stability
Lagrangian submanifolds Hamiltonian stability
2010/11/19
We apply the concept of castling transform of prehomogeneous vector spaces to produce new examples of minimal homogeneous Lagrangian submanifolds in the complex projective space. Furthermore we verify...
Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds
Time-dependent Mechanics presymplectic structures Poisson structures
2010/11/26
A description of time-dependent Mechanics in terms of Lagrangian submanifolds of presymplectic and Poisson manifolds is presented. Two new Tulczyjew triples are discussed. The first one is adapted to ...
Floer homology and its continuity for non-compact Lagrangian submanifolds
Floer homology non-compact Lagrangian submanifolds
2010/3/1
We give a construction of the Floer homology of the pair of vnon-compact Lagrangian submanifolds, which satisfies natural continuity property under the Hamiltonian isotopy that moves the infinity but ...
Lagrangian Submanifolds Foliated by $(n-1)$-Spheres in $\R^{2n}$
Lagrangian submanifold special Lagrangian self-similar Hamiltonian stationary
2007/12/12
We study Lagrangian submanifolds foliated by $(n-1)$-spheres in $\R^{2n}$ for $n \geq 3$. We give a general parametrization for such submanifolds, and refine that description when the submanifold is s...