Embeddedness of the solutions to the H-Plateau problem

作者：Coskunuzer Bans^*

来源：Advances in Mathematics, 2017, 317: 553-574.

DOI：10.1016/j.aim.2017.07.004

• Constant mean curvature
• H-disks
• H-Plateau problem
• Embeddedness
• Minimal surfaces
• H-surfaces

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

• 出版日期2017-9-7
• 单位MIT