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Given a sequence of asymptotically flat 3-manifolds of nonnegative scalarcurvature with outermost minimal boundary, converging in the pointed $C^0$Cheeger--Gromov sense to an asymptotically flat limit space, we show that thetotal mass of the limit is bounded above by the liminf of the total masses ofthe sequence. In other words, total mass is lower semicontinuous under suchconvergence. In order to prove this, we use Huisken's isoperimetric massconcept, together with a modified weak mean curvature flow argument. We includea brief discussion of Huisken's work before explaining our extension of thatwork. The results are all specific to three dimensions.

Lower semicontinuity of mass under $C^0$ convergence and Huisken's isoperimetric mass