  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.
