Minimal Lagrangian Diffeomorphisms Between Domains in the Hyperbolic Plane

Joint IAS/PU Geometric Analysis Seminar
Topic:	Minimal Lagrangian Diffeomorphisms Between Domains in the Hyperbolic Plane
Speaker:	Simon Brendle
Affiliation:	Stanford University
Date:	Tuesday, September 2
Time/Room:	3:00pm - 4:00pm/Fine Hall -- 314

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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 a circle.