Uniqueness and minimality of Euler's elastica with monotone curvature
Analysis of PDEs
2026-01-27 v2 Differential Geometry
Abstract
For an old problem of Euler's elastica we prove the novel global property that every planar elastica with non-constant monotone curvature is uniquely minimal subject to the clamped boundary condition. We also partly extend this unique minimality to the length-penalised case; this result is new even in view of local minimality. As an application we prove uniqueness of global minimisers in the straightening problem for generic boundary angles.
Keywords
Cite
@article{arxiv.2402.12771,
title = {Uniqueness and minimality of Euler's elastica with monotone curvature},
author = {Tatsuya Miura and Glen Wheeler},
journal= {arXiv preprint arXiv:2402.12771},
year = {2026}
}
Comments
21 pages, accepted version, to appear in JEMS