Generic uniqueness of area minimizing disks for extreme curves

Abstract

We show that for a generic nullhomotopic simple closed curve Gamma in the boundary of a compact, orientable. mean convex 3-manifold M with H-2(M, Z) = 0. there is a unique area minimizing disk D embedded in M with partial derivative D = Gamma. We also show that the same is true for nullhomologous curves in the absolutely area minimizing surface case.