Minimal Lagrangian diffeomorphisms between domains in the hyperbolic plane
Differential Geometry
2008-05-29 v2 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.0805.1897,
title = {Minimal Lagrangian diffeomorphisms between domains in the hyperbolic plane},
author = {S. Brendle},
journal= {arXiv preprint arXiv:0805.1897},
year = {2008}
}
Comments
revised version, to appear in J. Diff. Geom