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

Fabian Rupp

Fri Jul 16, 01:00-02:00 (2 months ago)

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. This is based on a joint work with Marius M\"uller (Albert-Ludwigs-Universit\"at Freiburg).

differential geometry

Audience: researchers in the topic

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