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The biharmonic hypersurface flow and the Willmore flow in higher dimensions

2025-06-03 11:30:33
报告人 时间 11:00-12:00
地点 E4-233 2025
月日 06-05

Time11:00-12:00, Thursday, June 5 2025

Venue:E4-233


Speaker: Min-Chun Hong, University of Queensland

Title:The biharmonic hypersurface flow and the Willmore flow in higher dimensions

Abstract: The biharmonic flow of hypersurfaces $M^n$ immersed in the Euclidean space $\mathbb {R}^{n+1}$ for $n\geq 2$ is given by a fourth order geometric evolution equation, which is similar to the Willmore flow. We apply the Michael-Simon-Sobolev inequality to establish new Gagliardo-Nirenberg inequalities on hypersurfaces. Based on these Gagliardo-Nirenberg inequalities, we apply local energy estimates to extend the solution by a covering argument and obtain an estimate on the maximal existence time of the biharmonic flow of hypersurfaces in higher dimensions. In particular, we solve a problem on the biharmonic hypersurface flow for $n=4$. Finally, we apply our new approach to prove global existence of the Willmore flow in higher dimensions. This is a joint work with Yu Fu and Gang Tian.