Title: Isoperimetricinequalities and nonlinear geometric evolution equations

Speaker: Prof. Guan Pengfei(McGill University) （加拿大皇家科学院院士）

Abstract: The isoperimetricinequality states that: for a domain $/Omega/subset /mathbb R^2$, $A(/Omega)/le/frac1{4/pi}L^2(/partial /Omega)$, where $A(/Omega)$ the area of $/Omega$ and$L(/partial /Omega)$ the perimeter of the boundary of $/Omega$. Moreover, theequality holds if and only if $/Omega$ is a round ball. There are manydifferent proofs of this classical inequality. One proof is by Gage-Hamilton,using curve shorting flow. This inequality (its higher dimensional version) isequivalent to the Sobolev inequality which is fundamental in analysis. Theinequality can be viewed a problem in calculus variations: what is the"optimal solution" and how to find a "good path" to thesolution. We will discuss how this type of problems naturally lead to some newnonlinear geometric evolutions equations, and how to use them to prove this andother geometric inequalities. Through example, one can see some deep connectionof nonlinear PDE and geometry. 

报告人简介：Pengfei Guan, is a Canadianmathematician and Canada Research Chair in Geometric Analysis. He's theDistinguished James McGill Professor at McGill University and a Fellow of RoyalSociety of Canada. Guan graduated from the Department of Mathematicsof Zhejiang University. From 1982 to 1984, Guan did graduate study at theInstitute of Mathematics of the Chinese Academy of Sciences in Beijing. From1984 to 1985, Guan studied at University of North Carolina at Chapel Hill inUSA. Guan later continued his study at Princeton University. Guan obtained MSin 1986 and PhD in 1989 both in mathematics from Princeton University. He wasemployed as Assistant Professor (1989-1993), Associate Professor(1993-1997), Professor (1997-2004) at McMaster University. Since 2004, hebecame Professor at McGill University. Guan was awarded the Alfred P. SloanFellowship from 1993 to 1995. Guan has held the Canada Research Chair since2004. Guan was elected to the Fellow of Royal Society of Canada in 2008. As amathematician, Prof. Guan works on nonlinear partial differential equationsand geometric analysis with particular interest in Monge-Ampere type equationsand published papers in Annals ofMathematics, Acta Math, Inventiones Mathematicae and other topjournals of mathematics.

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