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We prove that the set of closed finite gap curves in hyperbolic 3-space H³ is W2,2-dense in the Sobolev space of all closed W2,2-curves in H³. We also show that the set of closed finite gap curves in any two-dimensional space form E² is W2,2-dense in the Sobolev space of all closed W2,2-curves in E².
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Klein et al. (2020) studied this question.
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