A Li-Yau inequality for the 1-dimensional Willmore energy

Abstract

By the classical Li-Yau inequality, an immersion of a closed surface in ${\mathbb{R}}^n$ with Willmore energy below $8\pi$ has to be embedded. We discuss analogous results for curves in ${\mathbb{R}}^2$, involving Euler's elastic energy and other possible curvature functionals. Additionally, we provide applications to associated gradient flows.

Accepted version

References in corpus (1)

• The Lojasiewicz-Simon inequality for the elastic flow

Cited by in corpus (2)

• Li-Yau type inequality for curves in any codimension
• The critical points of the elastic energy among curves pinned at endpoints