A note on the regularity and the existence of Riemannian splines

2024/07/25 by Dario Corona, Corona, Dario, Roberto Giambò +3
Engineering · Immunology and Microbiology · Mathematics · #49J15 #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Biomarkers in Disease Mechanisms #Differential Geometry (math.DG) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2407.18408

openalex publication_date 2024/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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