Positive Mass Theorem for Graphs

Jiusen Liu 

Over the past several decades, much research has focused on understanding the relationship between the local energy density and the total mass of such a slice of a spacetime. Riemannian positive mass theorem is a well-known result. I will show you Lam's proof of the Positive mass theorem for Asymptotically flat graphs by recognizing the scalar curvature of such manifolds as a divergence. Furthermore, I will go further into Asymptotically hyperbolic graphs(AH Graphs), and introduce the total mass defined on such manifolds, then I will briefly talk about my project about proving the stability and positivity of mass in such AH Graphs.