讲座题目：The biharmonic hypersurface flow and the Willmore flow in higher dimensions
主讲人：Hong Min-Chun 教授
主持人：郑宇 教授
开始时间：2024-06-06 14:00
讲座地址：闵行校区数学馆102
主办单位：数学科学学院
报告人简介：
洪敏纯，澳大利亚昆士兰大学数学系教授，国际著名几何分析，偏微分方程专家。洪敏纯教授八十年代博士毕业于浙江大学，曾获第一届霍英东青年科学家奖，教育部自然科学一等奖。他在微分几何与非线性分析方面，特别在调和映射、Yang-Mills场、液晶模型偏微分方程等领域做出了杰出贡献，在国际上享有盛誉。在Adv. Math., Math.Ann., J. Funct. Anal.等国际顶尖学术期刊发表论文五十多篇。
报告内容：
The biharmonic flow of hypersurfaces $M^n$ immersed in the Euclidean space $\mathbb {R}^{n+1}$ for $n\geq 2$ is given by the fourth order geometric evolution equation, which is similar to the Willmore flow, but has an extra tangent part. 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 in \cite{BWW} 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 my joint work with Yu Fu and Gang Tian.
