Structure and classification results for the ∞-elastica problem

Roger Moser

doi:10.1353/ajm.2022.0030

Structure and classification results for the ∞-elastica problem

Roger Moser

Department of Mathematical Sciences

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Abstract

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.

Original language	English
Pages (from-to)	1299-1329
Number of pages	31
Journal	American Journal of Mathematics
Volume	144
Issue number	5
DOIs	https://doi.org/10.1353/ajm.2022.0030
Publication status	Published - 31 Oct 2022

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infinity-elastica-revised.pdf
This article appeared in the American Journal of Mathematics, Volume 144, Issue 5, Year, pages 1299-1329, Copyright © 2022, Johns Hopkins University Press.
Accepted author manuscript, 383 KB

http://arxiv.org/abs/1908.01569

Roger Moser
- R.Moserbath.acuk
- Department of Mathematical Sciences - Professor
Person: Research & Teaching

Cite this

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Structure and classification results for the ∞-elastica problem

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