  For two disjoint rectifiable star-shaped Jordan curves (including round
circles) in the asymptotic boundary of hyperbolic 3-space, if the distance (see
Definition 1.8) between these two Jordan curves are bounded from above by some
constant, then there exists an annulus-type area minimizing (or equivalently
least area) minimal surface asymptotic to these two Jordan curves. The main
results of this paper are Theorem 1.7 and Theorem 1.11.
