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

differential geometry

Audience: researchers in the topic

( video )

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The 2nd Geometric Analysis Festival

Series comments: Please, submit your questions to speakers at forms.gle/F8z5LjfNNwt3DD4i8

The recorded lecture videos are available at www.youtube.com/channel/UC2gHzqcv7CT1G3fa4a7sx-Q/playlists

Video Abstracts: youtu.be/uMBqmW4r8GE

For more details, please visit the webpage (will be updated later) at cosmogeometer.wordpress.com/geometric-analysis

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