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# Simon Brendle : Minimal Lagrangian diffeomorphisms between domains in the hyperbolic plane

Let $\Omega$ and $\tilde{\Omega}$ be domains in the hyperbolic plane with smooth boundary. Assume that both domains are uniformly convex, and have the same area. We show that there exists an area-preserving, orientation-preserving diffeomorphism $f: \Omega \to \tilde{\Omega}$ such that the graph of $f$ is a minimal surface in $\mathbb{H}^2 \times \mathbb{H}^2$. Moreover, we show that the set of all such diffeomorphisms is parametrized by the circle.

**Category**: Geometry and Topology**Duration**: 01:34:33**Date**: August 29, 2008 at 4:25 PM**Views**: 163-
**Tags:**seminar, Geometry/topology Seminar

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