  We show that for any simple closed curve in the sphere at infinity of a
Gromov hyperbolic 3-space with cocompact metric, there exist a properly
embedded least area plane in the space spanning the given curve. This gives a
positive answer to a conjecture of Gabai. Soma has already proven this
conjecture earlier. Our technique here is simpler and more general, and it can
be applied to many similar settings.
