The asymptotic Plateau problem in Gromov hyperbolic manifolds

We solve the asymptotic Plateau problem in every Gromov hyperbolic Hadamard manifold (X,g) with bounded geometry. That is, we prove existence of complete (possibly singular) k-dimensional area minimizing surfaces in X with prescribed boundary data at infinity, for a large class of admissible limit sets and for all $2 \le k < dim X$ . The result also holds with respect to any riemannian metric $\tilde g$ on X which is lipschitz equivalent to g.