A note on the regularity and the existence of Riemannian k-splines.
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| Title: | A note on the regularity and the existence of Riemannian k-splines. |
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| Authors: | Corona, D.1 (AUTHOR) dario.corona@unicam.it, Giambò, R.1 (AUTHOR) roberto.giambo@unicam.it, Piccione, P.2,3 (AUTHOR) paolo.piccione@usp.br |
| Source: | Mathematics of Control, Signals & Systems. Sep2025, Vol. 37 Issue 3, p661-695. 35p. |
| Subjects: | Riemannian manifolds, Splines, Critical point theory, Smoothness of functions, Mathematical optimization, Interpolation |
| Abstract: | In this paper, we present a comprehensive proof concerning the regularity of critical points for the spline energy functional on Riemannian manifolds, even for the general higher-order case. Although this result is widely acknowledged in the literature, a detailed proof was previously absent. Our proof relies on a generalization of the Lemma of DuBois-Reymond. Furthermore, we establish the existence of minimizers for the spline energy functional in cases where multiple interpolation points are prescribed alongside just one velocity. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics of Control, Signals & Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 188627132 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00498-025-00414-y Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 35 StartPage: 661 Subjects: – SubjectFull: Riemannian manifolds Type: general – SubjectFull: Splines Type: general – SubjectFull: Critical point theory Type: general – SubjectFull: Smoothness of functions Type: general – SubjectFull: Mathematical optimization Type: general – SubjectFull: Interpolation Type: general Titles: – TitleFull: A note on the regularity and the existence of Riemannian k-splines. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Corona, D. – PersonEntity: Name: NameFull: Giambò, R. – PersonEntity: Name: NameFull: Piccione, P. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 09324194 Numbering: – Type: volume Value: 37 – Type: issue Value: 3 Titles: – TitleFull: Mathematics of Control, Signals & Systems Type: main |
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