# 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

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.