English

The critical points of the elastic energy among curves pinned at endpoints

Differential Geometry 2021-06-25 v3 Analysis of PDEs Classical Analysis and ODEs

Abstract

In this paper we find curves minimizing the elastic energy among curves whose length is fixed and whose ends are pinned. Applying the shooting method, we can identify all critical points explicitly and determine which curve is the global minimizer. As a result we show that the critical points consist of wavelike elasticae and the minimizers do not have any loops or interior inflection points.

Keywords

Cite

@article{arxiv.2103.11607,
  title  = {The critical points of the elastic energy among curves pinned at endpoints},
  author = {Kensuke Yoshizawa},
  journal= {arXiv preprint arXiv:2103.11607},
  year   = {2021}
}

Comments

22 pages, 4 figures