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arXiv · 1908.01569

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

Roger Moser
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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.

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Roger Moser. 2019-08-05. Structure and classification results for the $\infty$-elastica problem. https://doi.org/10.1353/ajm.2022.0030

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