Minimal planes in hyperbolic space

摘要

In this paper we show a generic finiteness result for least area planes in H-3. Moreover, we prove that the space of minimal immersions of disk into H-3 is a submanifold of product bundle over a space of immersions of circle into S-infinity(2)(H-3) and the bundle projection map is when restricted to this submanifold is Fredholm of index zero. Using this, we also show that the space of minimal planes with smooth boundary curve at infinity is a manifold.