Minimal Planes in Hyperbolic Space

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.