  We show a generic finiteness result for least area planes in 3-dimensional
hyperbolic space. Moreover, we prove that the space of minimal immersions of
disk into hyperbolic space is a submanifold of a product bundle over a space of
immersions of circle into sphere at infinity. The bundle projection map when
restricted to this submanifold is Fredholm of index zero. By using this result,
we also show that the space of minimal planes with smooth boundary curve at
infinity is a manifold.
