TY - JOUR

T1 - Structure and classification results for the ∞-elastica problem

AU - Moser, Roger

N1 - Accepted for publication in the American Journal of Mathematics.

PY - 2021/7/27

Y1 - 2021/7/27

N2 - Consider the following variational problem: among all curves in Rn 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.

AB - Consider the following variational problem: among all curves in Rn 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.

M3 - Article

JO - American Journal of Mathematics

JF - American Journal of Mathematics

SN - 0002-9327

ER -