走向现代数学学术报告 - 邝国权博士（No. 531）

题目：A unified approach to discrete and smooth isoperimetric inequalities

报告人：邝国权 博士 （University of Wollongong）

时间：2022-10-13下午2:30

腾讯会议号：462-985-773

会议链接：https://meeting.tencent.com/dm/vUdj2DWuZcyz

摘要：The isoperimetric inequality states that for a simple closed curve of length $L$ on the plane which encloses a region of area $A$, the isoperimetric deficit $L^2 -4 \pi A$ is non-negative, and is zero if and only if it is a circle. In this talk I am going to demonstrate some sharp isoperimetric type inequalities involving not only the length and the area, but also its curvature and its derivatives of arbitrary order. The main ingredient is a higher order Wirtinger inequality which is proved using Fourier series. I will show that the same method can be applied to obtain isoperimetric inequalities for polygons as well. If time allows, I will also show some Minkowski type inequalities for hypersurfaces and a Chernoff type inequality for smooth curves.

报告人简介：邝国权，2011年博士毕业于香港中文大学数学系。博士毕业后在莫纳什大学、澳大利亚国立大学、迈阿密大学做博士后研究，曾任成功大学副教授，现任伍伦贡大学数学系讲师。主要研究几何分析及相关领域如数学广义相对、几何流及几何不等式。迄今在《Math. Ann.》、《Cal. Var. and PDE》、《Comm. Anal. Geom》《Math. Res. Lett.》等国际权威期刊发表文章近二十篇。