@article{Agostiniani2022, 
author = {Virginia Agostiniani and Lorenzo Mazzieri and Francesca Oronzio},
title = {A geometric capacitary inequality for sub-static manifolds with harmonic potentials},
year = {2022},
journal = {Mathematics in Engineering},
volume = {4},
number = {2},
pages = {1-40},
keywords = {sub–static metrics, splitting theorem, Schwarzschild solution, overdetermined boundary value problems},
url = {https://www.sciopen.com/article/10.3934/mine.2022013},
doi = {10.3934/mine.2022013},
abstract = {In this paper, we prove that associated with a sub-static asymptotically flat manifold endowed with a harmonic potential there is a one-parameter family    {      F          β        } of functions which are monotone along the level-set flow of the potential. Such monotonicity holds up to the optimal threshold    β  =            n      −      2              n      −      1       and allows us to prove a geometric capacitary inequality where the capacity of the horizon plays the same role as the ADM mass in the celebrated Riemannian Penrose Inequality.}
}