Properly embedded, area-minimizing surfaces in hyperbolic $3$-space

We prove prove a bridge principle at infinity for area-minimizing surfaces in the hyperbolic space ${\mathbb{H}}^3$, and we use it to prove that any open, connected, orientable surface can be properly embedded in ${\mathbb{H}}^3$ as an area-minimizing surface. Moreover, the embedding can be constructed in such a way that the limit sets of different ends are disjoint.