Hamiltonian stationary Lagrangian tori in Kähler manifolds

Adrian Butscher, J. Corvino

Journal of the Calculus of Variations and Partial Differential Equations


A Hamiltonian stationary Lagrangian submanifold of a Kähler manifold is a Lagrangian submanifold whose volume is stationary under Hamiltonian variations. We find a sufficient condition on the curvature of a Kähler manifold of real dimension four to guar- antee the existence of a family of small Hamiltonian stationary Lagrangian tori.

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