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arXiv · 2407.18408

A note on the regularity and the existence of Riemannian splines

Dario Corona·Roberto Giambò·Paolo Piccione
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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 DuBois-Reymond Lemma. Furthermore, we establish the existence of minimizers for the spline energy functional in cases where multiple interpolation points are prescribed alongside just one velocity.

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Dario Corona, Roberto Giambò, Paolo Piccione. 2024-07-25. A note on the regularity and the existence of Riemannian splines. https://arxiv.org/abs/2407.18408

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