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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