A Green's function proof of the Positive Mass Theorem

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. MSC (2020): 53C21, 31C12, 31C15, 53C24, 53Z05.

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