Inequalities for the ADM-mass and capacity of asymptotically flat manifolds with minimal boundary

摘要

We present some recent developments involving inequalities for the ADM-mass and capacity of asymptotically flat manifolds with boundary. New, more general proofs of classic Euclidean estimates are also included. The inequalities are rigid and valid in all dimensions, and constitute a step towards proving the Riemannian Penrose inequality in arbitrary dimensions.