## Columbia Mathematics Department
Colloquium

*Min-Oo's Conjecture for the
Hemisphere*

### by

### Simon Brendle

### Stanford and Princeton

Abstract:

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**