On closed finite gap curves in spaceforms II. Issue 1 (6th May 2020) - Klein, Sebastian; Kilian, Martin
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 $\mathbb{E}^{2}$ .