Hamiltonian stationary Lagrangian surfaces in C^2

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00795181
Contributor : Pascal Romon <>
Submitted on : Wednesday, February 27, 2013 - 3:10:15 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:04 PM

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Frédéric Hélein, Pascal Romon. Hamiltonian stationary Lagrangian surfaces in C^2. Communications in Analysis and Geometry, 2002, 10 (1), pp.79-126. ⟨10.4310/CAG.2002.v10.n1.a5⟩. ⟨hal-00795181⟩

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