Published Paper

Inserted: 24 may 2022
Last Updated: 24 may 2022

Journal: Mathematics in Engineering
Volume: 4
Number: 2
Pages: 40
Year: 2021
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 $\{F_{\beta}\}$ 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.

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• A geometric capacitary inequality for sub--static manifolds with harmonic potentials.pdf