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Mathematics > Analysis of PDEs
Title: A geometric capacitary inequality for sub-static manifolds with harmonic potentials
(Submitted on 18 Dec 2020)
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.
Submission history
From: Francesca Oronzio Miss. [view email][v1] Fri, 18 Dec 2020 10:55:07 GMT (38kb)
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