Uniqueness and minimality of Euler's elastica with monotone curvature
arXiv:2402.12771 · doi:10.4171/jems/1708
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.
arXiv comment21 pages, accepted version, to appear in JEMS