A boundary value problem for minimal Lagrangian graphs
Analysis of PDEs
2009-10-20 v3 Differential Geometry
Abstract
Let \Omega and \tilde{\Omega} be uniformly convex domains in \mathbb{R}^n with smooth boundary. We show that there exists a diffeomorphism f: \Omega \to \tilde{\Omega} such that the graph \Sigma = \{(x,f(x)): x \in \Omega\} is a minimal Lagrangian submanifold of \mathbb{R}^n \times \mathbb{R}^n.
Cite
@article{arxiv.0805.3715,
title = {A boundary value problem for minimal Lagrangian graphs},
author = {S. Brendle and M. Warren},
journal= {arXiv preprint arXiv:0805.3715},
year = {2009}
}
Comments
Final version, to appear in J. Diff. Geom