2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104944In 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.Differential GeometryMathematical Physics83C57; 53C44text