数学科学系

Department of Mathematical Sciences

How to simplify complicated plane curves

报告题目How to simplify complicated plane curves

 

报告人Professor Richard Schoen (斯坦福大学, 美国国家科学院院士)

 

时间2013425号(星期四)16:00-17:00

 

地点:理科楼数学系A404

 

摘要The curve-shortening flow has been much studied in differential geometry over the past 25 years. In this talk we will introduce the problem, which involves the flow of a plane curve in the normal direction with speed equal to the curvature. It was shown by M. Grayson in 1987 that the flow converts an arbitrary embedded closed curve into a circle! Over the next 10 years Grayson's proof was clarified and simplified by R. Hamilton and G. Huisken. In 2009, B. Andrews and P. Bryan gave a still more direct proof.

 

We will describe the main ingredient in these simplifications, which involves finding a geometric quantity that is improved under the flow and prevents the formation of certain types of singularities. Although this is a hard theorem, its proof uses only two-variable calculus and a lot of cleverness. The curve-shortening flow is the simplest of several geometric flows whose study is a topic of current research interest in differential geometry. These flows have certain features and methods in common, particularly with regard to the formation of singularities. This talk is intended for undergraduate mathematics students.

 

联系人:张友金