Embeddedness of the solutions to the H-Plateau Problem

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.

23 pages, 2 figures, minor changes

References in corpus (1)

• Curvature estimates for constant mean curvature surfaces

Cited by in corpus (2)

• Asymptotic H-Plateau Problem in Hyperbolic 3-space
• Embedded $H$-Planes in Hyperbolic 3-Space