Minimising maximum curvature

The student will study the minima or critical points of functionals involving the maximum (formulated in terms of the L-infinity norm) of the curvature of certain geometric objects such as curves in Riemannian manifolds. These are somewhat unconventional problems where many of the usual tools from functional analysis do not apply. The student will therefore explore alternative approaches to determine the structure and properties of the minima and/or critical points.