Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

On the Riemannian Penrose Inequality

Hongyi Sheng
Wednesday, November 13, 2019
5:00 pm - 5:50 pm
RH 510R

Talk Abstract:

On Apr. 10, 2019, astronomers captured the first image of a black hole. This was a huge progress, for once we know the area of the event horizon, we actually get an estimate of the mass of the black hole. In fact, earlier in 1973, R. Penrose conjectured that given the dominant energy condition, the total mass of a space-time which contains black holes with event horizons of total area A should be at least $\sqrt{A/16\pi}$. An important special case in Riemannian geometry is now known as the Riemannian Penrose inequality. This inequality was first established by G. Huisken and T. Ilmanen in 1997 using the inverse mean curvature flow for a single black hole and then by H. Bray in 1999 for any number of black holes, using the technique of a conformal flow. Later in 2009, H. Bray and D. Lee generalized Bray’s result to dimension up to 7. In this talk, we will mainly focus on the construction of Bray’s conformal flow in dimension 3. We will see that the area of the horizon is a constant along the flow, and that the mass is decreasing, using the well-known positive mass theorem (Schoen-Yau 79’). The convergence to the Schwarzschild metric finally gives us the inequality.

About the Speaker:

Hongyi is a fourth-year PhD student interested in geometric analysis. In his spare time, he likes traveling.

Refreshments:

Pizza will be served after the talk.