A Green's function proof of the Positive Mass Theorem

V. Agostiniani, L. Mazzieri, F. Oronzio

Published 2021-08-18Version 1

In this short note, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green's function of an asymptotically flat $3$-manifolds. In the same context and for $1<p<3$, a Geroch-type calculation is performed along the level sets of $p$-harmonic functions, leading to a new proof of the Riemannian Penrose Inequality in some case studies.