We will first discuss a generalized Positive Mass Theorem on a class ofpiecewise smooth asymptotically flat manifolds with broken mean curvatureacross a hypersurface. Then we will relate it to Bartnik's quasi-localmass definition and explain how Corvino's scalar curvaturedeformation theorem implies that a minimal mass extension, if exists,must be static. Finally, we will prove that, for any metric thatis close enough to the Euclidean metric on a ball and has reflectioninvariant boundary data, there always exists an asymptotically flat, scalar flat and static metric extension with Bartnik's geometric boundarycondition.