The $\infty$-elastica problem on a Riemannian manifold

Ed Gallagher; Roger Moser

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arXiv · 2202.07407

The $\infty$-elastica problem on a Riemannian manifold

Ed Gallagher·Roger Moser

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Abstract

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 $L^\infty$ 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.

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Ed Gallagher, Roger Moser. 2022-02-15. The $\infty$-elastica problem on a Riemannian manifold. https://arxiv.org/abs/2202.07407

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