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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 011, 29 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.011 (Mi sigma1548) 		 
On Closed Finite Gap Curves in Spaceforms I

Sebastian Kleina, Martin Kilianb

a Lehrstuhl für Mathematik III, Universität Mannheim, B 6, 28–29, 68131 Mannheim, Germany
b Department of Mathematics, University College Cork, Ireland
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DOI: https://doi.org/10.3842/SIGMA.2020.011
Abstract: We show that the spaces of closed finite gap curves in ${\mathbb R}^3$ and ${\mathbb S}^3$ are dense with respect to the Sobolev $W^{2,2}$-norm in the spaces of closed curves in ${\mathbb R}^3$ respectively ${\mathbb S}^3$.
Keywords: closed finite gap curves, integrable systems, nonlinear Schrödinger equation, asymptotic estimates.
Funding agency Grant number
Deutsche Forschungsgemeinschaft 414903103
Sebastian Klein is funded by the Deutsche Forschungsgemeinschaft, Grant 414903103.
Received: June 14, 2019; in final form February 28, 2020; Published online March 4, 2020
Bibliographic databases:
Document Type: Article
MSC: 53A04; 37K10; 30D15; 46E35; 22E46
Language: English
Citation: Sebastian Klein, Martin Kilian, “On Closed Finite Gap Curves in Spaceforms I”, SIGMA, 16 (2020), 011, 29 pp.
Citation in format AMSBIB
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