  Consider the following variational problem: among all curves in
$\mathbb{R}^n$ of fixed length with prescribed end points and prescribed
tangents at the end points, minimise the $L^\infty$-norm of the curvature. We
show that the solutions of this problem, and of a generalised version, are
characterised by a system of differential equations. Furthermore, we have a lot
of information about the structure of solutions, which allows a classification.
