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The research aims to address spline interpolation problems on smooth Riemannian manifolds using gradient flows.

February 20, 2026Mathematische AnnalenOpen Access

Higher-order Riemannian spline interpolation problems: a unified approach via gradient flows

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The research aims to address spline interpolation problems on smooth Riemannian manifolds using gradient flows.
Developed a unified approach utilizing gradient flows for spline interpolation and least-squares fitting.
Extended the method to variational spline interpolation problems on Lie groups.
Proved the existence of global solutions in Hölder spaces for the gradient flow.
Demonstrated that the asymptotic limits of solutions validate the variational spline interpolation problem.
Provided insights into potential numerical schemes for practical applicability of the approach.

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Implication

This approach addresses spline interpolation challenges in Riemannian manifolds, indicating implications for geometric control theory and statistical shape analysis.

Cite This Study

Lin et al. (2026) studied this question.

synapsesocial.com/papers/6997b911baf9c852d8c25fa3 https://doi.org/10.1007/s00208-026-03398-5

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Implication

This approach addresses spline interpolation challenges in Riemannian manifolds, indicating implications for geometric control theory and statistical shape analysis.

Higher-order Riemannian spline interpolation problems: a unified approach via gradient flows

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Discussion

Implication

Cite This Study

Higher-order Riemannian spline interpolation problems: a unified approach via gradient flows

Key Points

Discussion

Implication

Cite This Study

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