Hamiltonian stationary Lagrangian surfaces in C^2

By Frédéric Hélein, Pascal Romon. 2000

115 citations recorded by the source corpus.

We study Hamiltonian stationary Lagrangian surfaces in C^2, i.e. Lagrangian surfaces in C^2 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.

View Paper: https://www.semanticscholar.org/paper/fbde2be65c863b77e90ed15729b708f7c0401f30

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Citations in the corpus

• Toric Topology (2012, background): “More examples of H-minimal Lagrangian submanifolds in a complex space were constructed in the works [64], [130], [4], among others.”
• Constrained Willmore tori in the 4-sphere (2008, background): “It is shown in [ 16 ] that f is Hamiltonian stationary Lagrangian (i.e., a Lagrangian immersion that is stationary for the area functional under all Hamiltonian variations) if and only if β is harmonic.”