The elastica problem under area constraint
Optimization and Control
2015-01-13 v2
Abstract
We show that the elastic energy of a closed curve has a minimizer among all plane simple regular closed curves of given enclosed area , and that the minimum is attained for a circle. The proof is of a geometric nature and deforms parts of in a finite number of steps to construct some related convex sets with smaller energy.
Cite
@article{arxiv.1411.6100,
title = {The elastica problem under area constraint},
author = {Vincenzo Ferone and Bernd Kawohl and Carlo Nitsch},
journal= {arXiv preprint arXiv:1411.6100},
year = {2015}
}