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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 09324194 |
| DOI: | 10.1007/s00498-025-00414-y |
