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arXiv · 1005.1723

Embedded Plateau Problem

Baris Coskunuzer
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Abstract

We show that if C is a simple closed curve bounding an embedded disk in a closed 3-manifold M, then there exists a disk D in M with boundary C such that D minimizes the area among the embedded disks with boundary C. Moreover, D is smooth, minimal and embedded everywhere except where the boundary C meets the interior of D. The same result is also valid for homogenously regular manifolds with sufficiently convex boundary.

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Baris Coskunuzer. 2010-05-11. Embedded Plateau Problem. https://doi.org/10.1090/s0002-9947-2011-05486-3

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