Sebastian Klein, Martin Kilian, “On Closed Finite Gap Curves in Spaceforms I”, SIGMA, 2020, Volume 16,011, 29 pp.

On Closed Finite Gap Curves in Spaceforms I

Sebastian Klein^a, 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

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.

MSC: 53A04; 37K10; 30D15; 46E35; 22E46

Received: June 14, 2019; in final form February 28, 2020; Published online March 4, 2020

Language: English

DOI: 10.3842/SIGMA.2020.011