Minimal Planes in Hyperbolic Space

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.

Full Text (PDF format)

Published 1 January 2004