*Accepted Paper*

**Inserted:** 23 may 2022

**Last Updated:** 28 jan 2024

**Journal:** Communications in Mathematical Physics

**Year:** 2021

**Abstract:**

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.

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