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 {Fβ} of functions which are monotone along the level-set flow of the potential. Such monotonicity holds up to the optimal threshold β = n/n2/1 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.

A geometric capacitary inequality for sub-static manifolds with harmonic potentials / Agostiniani, Virginia; Mazzieri, Lorenzo; Oronzio, Francesca. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - 2022, 4:2(2022), pp. 1-40. [10.3934/mine.2022013]

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

Agostiniani, Virginia;Mazzieri, Lorenzo;Oronzio, Francesca
2022-01-01

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 {Fβ} of functions which are monotone along the level-set flow of the potential. Such monotonicity holds up to the optimal threshold β = n/n2/1 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.
2022
2
Agostiniani, Virginia; Mazzieri, Lorenzo; Oronzio, Francesca
A geometric capacitary inequality for sub-static manifolds with harmonic potentials / Agostiniani, Virginia; Mazzieri, Lorenzo; Oronzio, Francesca. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - 2022, 4:2(2022), pp. 1-40. [10.3934/mine.2022013]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/315302
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