On Closed Finite Gap Curves in Spaceforms I

We show that the spaces of closed finite gap curves in ℝ³ and S³ are dense with respect to the Sobolev W²'²-norm in the spaces of closed curves in ℝ³, respectively S³.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2020
Hauptverfasser: Klein, Sebastian, Kilian, Martin
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2020
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/210599
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:On Closed Finite Gap Curves in Spaceforms I. Sebastian Klein and Martin Kilian. SIGMA 16 (2020), 011, 29 pages

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1862730845805084672
author Klein, Sebastian
Kilian, Martin
author_facet Klein, Sebastian
Kilian, Martin
citation_txt On Closed Finite Gap Curves in Spaceforms I. Sebastian Klein and Martin Kilian. SIGMA 16 (2020), 011, 29 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We show that the spaces of closed finite gap curves in ℝ³ and S³ are dense with respect to the Sobolev W²'²-norm in the spaces of closed curves in ℝ³, respectively S³.
first_indexed 2025-12-17T12:04:19Z
format Article
fulltext
id nasplib_isofts_kiev_ua-123456789-210599
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-17T12:04:19Z
publishDate 2020
publisher Інститут математики НАН України
record_format dspace
spelling Klein, Sebastian
Kilian, Martin
2025-12-12T10:36:47Z
2020
On Closed Finite Gap Curves in Spaceforms I. Sebastian Klein and Martin Kilian. SIGMA 16 (2020), 011, 29 pages
1815-0659
2020 Mathematics Subject Classification: 53A04; 37K10; 30D15; 46E35; 22E46
arXiv:1801.07032
https://nasplib.isofts.kiev.ua/handle/123456789/210599
https://doi.org/10.3842/SIGMA.2020.011
We show that the spaces of closed finite gap curves in ℝ³ and S³ are dense with respect to the Sobolev W²'²-norm in the spaces of closed curves in ℝ³, respectively S³.
We thank Martin U. Schmidt for useful discussions and his idea of using perturbed Fourier coefficients. We also thank the referees for their insightful remarks and helpful suggestions that improved the final presentation of the results in this paper. Sebastian Klein is funded by the Deutsche Forschungsgemeinschaft, Grant 414903103.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
On Closed Finite Gap Curves in Spaceforms I
Article
published earlier
spellingShingle On Closed Finite Gap Curves in Spaceforms I
Klein, Sebastian
Kilian, Martin
title On Closed Finite Gap Curves in Spaceforms I
title_full On Closed Finite Gap Curves in Spaceforms I
title_fullStr On Closed Finite Gap Curves in Spaceforms I
title_full_unstemmed On Closed Finite Gap Curves in Spaceforms I
title_short On Closed Finite Gap Curves in Spaceforms I
title_sort on closed finite gap curves in spaceforms i
url https://nasplib.isofts.kiev.ua/handle/123456789/210599
work_keys_str_mv AT kleinsebastian onclosedfinitegapcurvesinspaceformsi
AT kilianmartin onclosedfinitegapcurvesinspaceformsi