Generic Uniqueness of Area Minimizing Disks for Extreme Curves

Details Generic Uniqueness of Area Minimizing Disks for Extreme Curves Generic Uniqueness of Area Minimizing Disks for Extreme Curves

2008-10-28

arxiv.org/abs/0810.4985v2

American J. Math. 132 (2010) 1091-1104

Mathematics

Differential Geometry

15 pages

Scientific paper

10.1353/ajm.0.0129

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.

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