The Sigma-Inverse Mean Curvature Flow and the Generalized Penrose Conjecture

The generalized Penrose conjecture for initial data sets satisfying the dominant energy condition asserts that the ADM mass is bounded below by a quantity involving the area of the outermost generalized apparent horizon. In this talk, I will discuss my recent results in two new special cases: when the second fundamental form of the initial data set has vanishing trace-free part, and when it is 2-convex. The main tools are sigma-inverse mean curvature flow and an associated monotonicity formula.