Quasi-local mass and the existence of horizons

In this paper, we obtain lower bounds for the Brown-York quasilocal mass and the Bartnik quasilocal mass for compact three manifolds with smooth boundaries. As a consequence, we derive sufficient conditions for the existence of horizons for a certain class of compact manifolds with boundary and some asymptotically flat complete manifolds.The method is based on analyzing Hawking mass and inverse mean curvature flow.