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.
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210599 |
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| 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 |
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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.
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| 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 |