Hamiltonian stationary Lagrangian surfaces in C²

2000/09/22 by Frederic Helein, Helein, Frederic, Pascal Romon +1 · 2 citations
Mathematics · #53C42 (Primary) 58E20 #58F07 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C42 #msc:58E20 #msc:58F07

paper · pdf · doi:10.48550/arxiv.math/0009202

3 figures

arxiv created 2000/09/22 · arxiv updated 2009/11/30

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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• Optimal Regularity for Hölder continuous Hamiltonian Stationary Lagrangian graphs
• Minimal Lagrangian surfaces in the two dimensional complex quadric via the loop group method

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