Resumen de Uniqueness of area minimizing surfaces for extreme curves

Baris Coskunuzer, Tolga Etgü

• Let M be a compact, orientable, mean convex 3-manifold with boundary ∂M. We show that the set of all simple closed curves in ∂M which bound unique area minimizing disks in M is dense in the space of simple closed curves in ∂M which are nullhomotopic in M. We also show that the set of all simple closed curves in ∂M which bound unique absolutely area minimizing surfaces in M is dense in the space of simple closed curves in ∂M which are nullhomologous in M.