Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 011, 29 pages      arXiv:1801.07032      https://doi.org/10.3842/SIGMA.2020.011

On Closed Finite Gap Curves in Spaceforms I

Sebastian Klein a and Martin Kilian b
a)  Lehrstuhl für Mathematik III, Universität Mannheim, B 6, 28-29, 68131 Mannheim, Germany
b)  Department of Mathematics, University College Cork, Ireland

Received June 14, 2019, in final form February 28, 2020; Published online March 04, 2020

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 ${\mathbb S}^3$.

Key words: closed finite gap curves; integrable systems; nonlinear Schrödinger equation; asymptotic estimates.

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