On closed finite gap curves in spaceforms II

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Date
2020-05-06
Authors
Klein, Sebastian
Kilian, Martin
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Oxford University Press
Published Version
10.1093/integr/xyaa002
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Abstract
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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Keywords
Integrable systems , Finite gap , Non-linear Schroedinger equation , Backlund transformation
Citation
Klein, S. and Kilian, M. (2020) 'On closed finite gap curves in spaceforms II', Journal of Integrable Systems, 5(1), xyaa002 (25pp). doi: 10.1093/integr/xyaa002
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https://hdl.handle.net/10468/15088
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Mathematical Sciences- Journal Articles
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© 2020, the authors. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com