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