The infty -Elastica Problem on a Riemannian Manifold

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 endpoints and tangents at the endpoints, 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.