A new boundary mass for asymptotically flat half-manifolds

We introduce a boundary analogue of the Gauss–Bonnet–Chern mass for asymptotically flat half-manifolds with non-compact boundary. We prove that this mass is well defined and establish the corresponding positive mass theorems for graphical and conformally flat graphs. Also we provide a Penrose-type inequality for the mass ${\mathfrak{m}}_{a,B}(g)$.