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arXiv · 1504.00661

Embeddedness of the solutions to the H-Plateau Problem

Baris Coskunuzer
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Abstract

We generalize Meeks and Yau's embeddedness result on the solutions of the Plateau problem to the constant mean curvature disks. We show that any minimizing H-disk in an H_0-convex domain is embedded for any H in [0,H_0). In particular, for the unit ball B in R^3, this implies that for any H in [0,1], any Jordan curve in the unit sphere bounds an embedded H-disk in B.

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Baris Coskunuzer. 2017-02-16. Embeddedness of the solutions to the H-Plateau Problem. https://doi.org/10.1016/j.aim.2017.07.004

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