Abstract
Abstract We prove that the set of closed finite gap curves in hyperbolic 3-space $\mathbb{H}^{3}$ is $W^{2,2}$-dense in the Sobolev space of all closed $W^{2,2}$-curves in $\mathbb{H}^{3}$. We also show that the set of closed finite gap curves in any two-dimensional space form $\mathbb{E}^{2}$ is $W^{2,2}$-dense in the Sobolev space of all closed $W^{2,2}$-curves in $\mathbb{E}^{2}$.
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