Quasicircles and quasiperiodic surfaces in pseudo-hyperbolic spaces

We study in this paper quasiperiodic maximal surfaces pseudo-hyperbolic spaces and show that they are characterised by a curvature condition, Gromov hyperbolicity or conformal hyperbolicity. the limit curves of these Einstein Universe admits canonical quasisymmetric parametrisation, while conversely every curve bounds surface such way parametrisation is continuous extension uniformisation; we give applications results to asymptotically hyperbolic surfaces, rigidity Anosov representations version universal Teichmüller space.