# Structure and classification results for the $\infty$-elastica problem

## TL;DR

This paper studies the $
abla$-elastica problem, characterizing solutions via differential equations and providing a classification of these solutions based on their structural properties.

## Contribution

It introduces a differential equation framework for the $
abla$-elastica problem and offers a comprehensive classification of solutions, extending previous understanding.

## Key findings

- Solutions are characterized by a specific system of differential equations.
- The structure of solutions allows for a detailed classification.
- The results apply to a generalized version of the problem.

## Abstract

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.