A spacetime positive mass theorem with corners via mollification

We prove a strict dominant energy deformation theorem for asymptotically flat initial data with corners along a hypersurface $\mathrm{\Sigma }$. The deformation preserves a corner condition on the Bartnik data across $\mathrm{\Sigma }$. We show that if the dominant energy condition holds on each side of $\mathrm{\Sigma }$ and the Bartnik data satisfy this corner condition, then the exterior end satisfies $E\ge \mathrm{\mid }P\mathrm{\mid }$ in every dimension $n\ge 3$.