Séminaire Géométrie et groupes discrets

# Quasi-circles and Maximal Surfaces in the Pseudo-hyperbolic Space

## by Prof. Jérémy Toulisse (Université de Nice-Sophia Antipolis)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description
Quasi-circles in the complex plane are fundamental objects in complex analysis; they were used by Bers to define an infinite-dimensional analogue of the usual Teichmüller space. After introducing the notion of quasi-circles in the boundary of the pseudo-hyperbolic space $H^{2,n}$, I will explain how to construct a unique complete maximal surface in $H^{2,n}$ bounded by a given quasi-circle. This construction relies on Gromov's theory of pseudo-holomorphic curves and provides a generalization of maximal representations of surface groups into rank 2 Lie groups. This joint work with François Labourie and Mike Wolf.
Organized by

Fanny Kassel

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