Uniqueness problem in geometric analysis and Lojasiewicz inequality

Abstract: Lojasiewicz inequality is an inequality in real algebraic geometry. It was first discovered by Leon Simon that Lojasiewicz inequality can be used to prove uniqueness of critical points in the problem of calculus of variation. In these lectures I will first introduce the Lojasiewicz inequality; then I will discuss the infinite dimensional Lojasiewicz inequality proved by Leon Simon in the setting of calculus of variations; then I will discuss some applications of Lojasiewicz inequality to prove the uniqueness of some geometric object; finally, I will discuss joint work with Jonathan Zhu on proving Lojasiewicz inequality finding an explicit power of the Lojasiewicz inequality near special self-shrinkers of mean curvature flow.

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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