Open AccessA geometric capacitary inequality for sub-static manifolds with harmonic potentials
Author(s) -
Virginia Agostiniani,
Lorenzo Mazzieri,
Francesca Oronzio
Publication year - 2021
Publication title -
mathematics in engineering
Language(s) - English
Resource type - Journals
ISSN - 2640-3501
DOI - 10.3934/mine.2022013
Subject(s) - mathematics , monotone polygon , monotonic function , harmonic , harmonic mean , manifold (fluid mechanics) , pure mathematics , harmonic function , mathematical analysis , combinatorics , geometry , physics , quantum mechanics , mechanical engineering , engineering
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_{\beta}\} $ of functions which are monotone along the level-set flow of the potential. Such monotonicity holds up to the optimal threshold $ \beta = \frac{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.