Structure and classification results for the ∞-elastica problem
Roger Moser · American Journal of Mathematics · 2022
We consider the following variational problem: among all curves in R n of fixed length with prescribed end points and prescribed tangents at the end points, minimise the L ∞ -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.