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 |
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Pages (from-to) | 1299-1329 |
Number of pages | 31 |
Journal | American Journal of Mathematics |
Volume | 144 |
Issue number | 5 |
DOIs | |
Publication status | Published - 31 Oct 2022 |