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

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

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 $...

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Bibliographic Details
Published in:Mathematics in engineering Vol. 4; no. 2; pp. 1 - 40
Main Authors: Agostiniani, Virginia, Mazzieri, Lorenzo, Oronzio, Francesca
Format: Journal Article
Language:English
Published: AIMS Press 01-03-2022
Subjects:
overdetermined boundary value problems
schwarzschild solution
splitting theorem
sub–static metrics
Online Access:Get full text
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Summary: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.
ISSN:2640-3501
2640-3501
DOI:10.3934/mine.2022013