Calculus of Variations and Geometric Measure Theory

V. Agostiniani - L. Mazzieri - F. Oronzio

A Green's function proof of the positive mass theorem

created by oronzio on 23 May 2022
modified on 28 Jan 2024


Accepted Paper

Inserted: 23 may 2022
Last Updated: 28 jan 2024

Journal: Communications in Mathematical Physics
Year: 2021


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.