The ∞-elastica problem on a Riemannian manifold

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We consider the following problem: on any given complete Riemannian manifold (M,g), among all curves which have fixed length as well as fixed end-points and tangents at the end-points, minimise the L∞ norm of the curvature. We show that the solutions of this problem, as well as a wider class of curves, must satisfy a second order ODE system. From this system we obtain some geometric information about the behaviour of the curves.
Original languageEnglish
Article number226
Number of pages26
JournalJournal of Geometric Analysis
Publication statusPublished - 3 May 2023


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