國立清華大學 數學系

Abstract: 

The isoperimetric inequality for domains in R^n is one of the most beautiful results in geometry.  In this talk, I will first review a beautiful argument of Xavier Cabré.  Next, I will discuss a recent development by Simon Brendle, who generalizes the previous argument to prove an isoperimetric inequality for minimal submanifolds of the Euclidean space.  Finally, I will talk about a version of isoperimetric inequality for maximal spacelike submanifolds of the Lorentzian space.  This is based on a joint work with Kai-Hsiang Wang.