Minimal graphs and harmonic diffeomorphisms.

Minimal graphs and harmonic diffeomorphisms.

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Harold Rosenberg, IMPA
Fine Hall 314

In 1952, Heinz gave another proof of Bernstein's Theorem ( an entire minimal graph over the euclidean plane is a plane) by showing there is no harmonic diffeomorphism from the disc onto the euclidean plane. Since then the existence theory of harmonic diffeomorphisms between closed surfaces has been developed and useful. In this talk I will use minimal graphs to obtain harmonic diffeomorphisms between complete surfaces of finite topology.