The pseudo-hyperbolic space $H^{2,n}$ is the pseudo-Riemannian analogue of the classical hyperbolic space. In this talk, I will explain how to solve an asymptotic Plateau problem in this space: given a topological circle in the boundary at infinity of $H^{2,n}$, we construct a unique complete maximal surface bounded by this circle. This construction relies on Gromov’s theory of pseudo-holomorphic curves. This is a joint work with François Labourie and Mike Wolf.

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Last updated: 24 Mar 2023