## Speaker:

Yiyue Zhang

## Institution:

UC Irvine

## Time:

Tuesday, October 12, 2021 - 4:00pm

## Location:

NS2 1201

I will introduce the harmonic level set method developed by Stern in 2019.

This technique has been used to prove the positive mass theorems in various

settings, for example, the Riemannian case, the spacetime case, the

hyperbolic case, and the positive mass theorem with charge. I will focus on

the positive mass theorem for asymptotically hyperbolic manifolds. We give a

lower bound for the mass in the asymptotically hyperbolic setting. In this

setting, we solve the spacetime harmonic equation and give an explicit

expansion for the solution. We also prove some rigidity results as

corollaries. This is joint work with Bray, Hirsch, Kazaras, and Khuri.