Communications in Analysis and Geometry
Volume 12 (2004)
Minimal Planes in Hyperbolic Space
Pages: 821 – 836
In this paper we show a generic finiteness result for least area planes in ℍ3. Moreover, we prove that the space of minimal immersions of disk into ℍ3 is a submanifold of product bundle over a space of immersions of circle into S2∞ (ℍ3) 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.