Generic non-uniqueness of complete $H$-surfaces embedded in ${\mathbb{H}}^3$

Abstract

We prove that, given $|H|<1$, a generic simple closed curve embedded in the asymptotic boundary of ${\mathbb{H}}^3$ (with respect to the supremum metric) bounds more than one complete surface embedded in ${\mathbb{H}}^3$ which has constant mean curvature $H$. We remark that this is not true for the space of simple closed ${\text{C}}^1$-curves.

9 pages, 2 figures

References in corpus (1)

• On the Number of Solutions to Asymptotic Plateau Problem