Quasi-local mass functionals and generalized inverse mean curvature flow, Omitted from published version

LetM be an asymptotically flat 3-manifold with nonnegative scalar curvature. In [4] Hubert Bray defines a family of quasi-local mass func-tionals which are monotone for surfaces smoothly satisfying a certain generalization of inverse mean curvature flow in M. We show that a weak solution in the sense of Huisken-Ilmanen [8] exists for a wide class of flows including these with monotone quasi-local mass function-als, and we show that the monotonicity holds for the weak flow as well. As shown in [4], a Penrose-type inequality for connected surfaces is an immediate corollary