Embedded Plateau Problem

Details Embedded Plateau Problem Embedded Plateau Problem

2010-05-11

arxiv.org/abs/1005.1723v2

Trans. Amer. Math. Soc. 364 (2012) 1211-1224

Mathematics

Differential Geometry

Scientific paper

10.1090/S0002-9947-2011-05486-3

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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