| Résume | The pseudo-hyperbolic space H^{2,n} is in many ways a generalisation of the hyperbolic space. It is a pseudo-Riemannian manifold with signature
(2,n) with constant curvature, it also has a « boundary at infinity ».
We explain in this joint work with Jérémy Toulisse and Mike Wolf how special curves in this boundary at infinity, bounds unique maximal surfaces in H^{2,n}. The result bears some analogy with the Cheng-Yau existence results for affine spheres tangent to convex curves in the projective plane. The talk will spend sometime explainig the geometry of the pseudo-hyperbolic space and its boundary at infinity, as well as description of maximal surfaces. If time permits, I will explain some extension to « quasi-periodic » maximal surfaces in H^{2,n}. |
