Hamiltonian stationary Lagrangian surfaces in C2
Abstract
We study Hamiltonian stationary Lagrangian surfaces in C2, i.e. Lagrangian surfaces in C2 which are stationary points of the area functional under smooth Hamiltonian variations. Using loop groups, we propose a formulation of the equation as a completely integrable system. We construct a Weierstrass type representation and produce all tori through either the integrable systems machinery or more direct arguments.
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