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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• A Green@s function proof of the positive mass theorem.pdf