  We show that for any extreme curve in a 3-manifold M, there exist a canonical
mean convex hull containing all least area disks spanning the curve. Similar
result is true for asymptotic case in hyperbolic 3-space such that for any
asymptotic curve, there is a canonical mean convex hull containing all minimal
planes spanning that curve. Applying this to quasi-Fuchsian manifolds, we show
that for any quasi-Fuchsian manifold, there exist a canonical mean convex core
capturing all essential minimal surfaces. On the other hand, we also show that
for a generic C^3-smooth curve in the boundary of C^3-smooth mean convex domain
in R^3, there exist a unique least area disk spanning the curve.
