Elastic curves and self-intersections
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.03020
- arXiv:
- arXiv:2408.03020
- Bibcode:
- 2024arXiv240803020M
- Keywords:
-
- Mathematics - Analysis of PDEs;
- Mathematics - Differential Geometry;
- 53A04;
- 49Q10;
- and 53E40
- E-Print:
- 32 pages, 6 figures, an expository note to appear in 2024 MATRIX Annals