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<p>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.</p>

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A note on the regularity and the existence of Riemannian k-splines

  • 期刊论文

  • 发表日期：

    2025年5月2日

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  • D. Corona,
  • R. Giambò,
  • P. Piccione

摘要

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.