A boundary value problem for minimal Lagrangian graphs

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Authors
Brendle, S.
Warren, M.
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Abstract
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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.
Comment: Final version, to appear in J. Diff. Geom
Keywords
Mathematics - Analysis of PDEs, Mathematics - Differential Geometry
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