Generic Uniqueness of Area Minimizing Disks for Extreme Curves

Abstract

We show that for a generic nullhomotopic simple closed curve C in the boundary of a compact, orientable, mean convex 3-manifold M with trivial second homology, there is a unique area minimizing disk D embedded in M where the boundary of D is C. We also show that the same is true for absolutely area minimizing surfaces.

15 pages

Cited by in corpus (3)

• Embeddedness of the solutions to the H-Plateau Problem
• Embedded $H$-Planes in Hyperbolic 3-Space
• Examples of Area Minimizing Surfaces in 3-manifolds