On closed finite gap curves in spaceforms II. Issue 1 (6th May 2020)

• Record Type: Journal Article
• Authors: Klein, Sebastian; Kilian, Martin
• Editors: Dunajski, Maciej
• Is Part Of: Journal of integrable systems. Volume 5:Issue 1(2020)
• Publication Date: 2020-05-06
• Subjects: integrable systems -- finite gap -- non-linear Schroedinger equation -- Backlund transformation; 53A04 -- 37K10 -- 37K15 -- 30D15 -- 46E35 -- 22E46; Mathematics -- Periodicals; 510
• DOI: 10.1093/integr/xyaa002
• Languages: English
• ISSNs: 2058-5985

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 $\mathbb{E}^{2}$ .