Generic uniqueness of area minimizing disks for extreme curves

Abstract

We show that for a generic nullhomotopic simple closed curve Γ in the boundary of a compact, orientable, mean convex 3-manifold M with H2(M, Z) = 0, there is a unique area minimizing disk D embedded in M with ∂D = Γ. We also show that the same is true for nullhomologous curves in the absolutely area minimizing surface case.