  We show that any noncompact oriented surface is homeomorphic to the leaf of a
minimal foliation of a closed $3$-manifold. These foliations are (or are
covered by) suspensions of continuous minimal actions of surface groups on the
circle. Moreover, the above result is also true for any prescription of a
countable family of topologies of open surfaces: they can coexist in the same
minimal foliation. All the given examples are hyperbolic foliations, meaning
that they admit a leafwise Riemannian metric of constant negative curvature.
Many oriented Seifert manifolds with a fibered incompressible torus and whose
associated orbifold is hyperbolic admit minimal foliations as above. The given
examples are not transversely $C^2$-smoothable.
