On the Rigidity of Riemannian-Penrose Inequality for Asymptotically Flat 3-manifolds with Corners

In this paper we prove a rigidity result for the equality case of the Penrose inequality on $3$-dimensional asymptotically flat manifolds with nonnegative scalar curvature and corners. Our result also has deep connections with the equality cases of Theorem 1 in \cite{Miao2} and Theorem 1.1 in \cite{LM}.