English

Elastic curves and self-intersections

Analysis of PDEs 2025-11-19 v3 Differential Geometry

Abstract

This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-intersecting curves in Euclidean space. We also discuss some open problems in related topics.

Keywords

Cite

@article{arxiv.2408.03020,
  title  = {Elastic curves and self-intersections},
  author = {Tatsuya Miura},
  journal= {arXiv preprint arXiv:2408.03020},
  year   = {2025}
}

Comments

32 pages, 6 figures, final version, an expository note to appear in 2024 MATRIX Annals

R2 v1 2026-06-28T18:05:09.519Z