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

Year: 2016
Type: preprint
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.
DOI: 10.48550/arxiv.1602.02006
Language: English
Open Access status: green
OpenAlex ID: W2270868358
Cites: 14
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Related to: 10