Minimal Lagrangian diffeomorphisms between domains in the hyperbolic plane

Details Minimal Lagrangian diffeomorphisms between domains in the hyperbolic plane Minimal Lagrangian diffeomorphisms between domains in the hyperbolic plane

2008-05-13

arxiv.org/abs/0805.1897v2

Mathematics

Differential Geometry

revised version, to appear in J. Diff. Geom

Scientific paper

Let N be a complete, simply-connected surface of constant curvature \kappa
\leq 0. Moreover, suppose that \Omega and \tilde{\Omega} are strictly convex
domains in N with the same area. We show that there exists an area-preserving
diffeomorphism from \Omega to \tilde{\Omega} whose graph is a minimal
submanifold of N \times N.

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