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Generic uniqueness of area minimizing disks for extreme curves

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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.

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Johns Hopkins University (JHU) Press

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Mathematics

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American Journal of Mathematics

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10.1353/ajm.0.0129

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