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arXiv · 1207.4695

Uniqueness of Area Minimizing Surfaces for Extreme Curves

Baris Coskunuzer·Tolga Etgü
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Abstract

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

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BibTeXRIS

Baris Coskunuzer, Tolga Etgü. 2012-07-19. Uniqueness of Area Minimizing Surfaces for Extreme Curves. https://doi.org/10.4171/rmi%2F810

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