Positive Mass Theorem on Manifolds admitting Corners along a Hypersurface

We study a class of non-smooth asymptotically flat manifolds on which metrics fails to be $C^1$ across a hypersurface $Σ$. We first give an approximation scheme to mollify the metric, then we prove that the Positive Mass Theorem still holds on these manifolds if a geometric boundary condition is satisfied by metrics separated by $Σ$.

No reviews yet.

No comments yet.