Columbia Mathematics Department Colloquium


Min-Oo's Conjecture for the Hemisphere


 Simon Brendle  

                                                               Stanford and Princeton



Consider a Riemannian metric on the hemisphere $S_+^n$ which has scalar curvature at least $n(n-1)$ and agrees with

 the standard metric in a neighborhood of the boundary. It was conjectured by Min-Oo that any metric with these properties

 must be isometric to the standard metric on the hemisphere. This conjecture is inspired by the positive mass theorem in

general relativity, and has been verified in many special cases. In this lecture, I will discuss the background of Min-Oo's

conjecture, and give a survey of various rigidity results involving scalar curvature. I will then describe joint work with

 F.C. Marques and A. Neves, which gives a complete answer to Min-Oo's Conjecture in dimension $n \geq 3$.


  Dec. 1st, Wednesday, 5:00-6:00 pm

Mathematics 520

Tea will be served at 4:30pm