English

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.

Keywords

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

R2 v1 2026-06-21T10:43:43.318Z