In the setting of Riemannian manifolds with nonnegative Ricci curvature, we provide geometric inequalities as consequences of the Monotonicity Formulas holding along the flow of the level sets of the p-capacitary potential. The work is divided into three parts. (1) In the first part, we describe the asymptotic behaviour of the p-capactitary potential in a natural class of Riemannian manifolds. (2) The second part is devoted to the proof of our Monotonicity-Rigidity Theorems. (3) In the last part, we apply the Monotonicity Theorems to obtain geometric inequalities, focusing on the Extended Minkowski Inequality.

Monotonicity Formulas in Nonlinear Potential Theory and their geometric applications / Benatti, Luca. - (2022 Jun 09), pp. 1-145. [10.15168/11572_346959]

Monotonicity Formulas in Nonlinear Potential Theory and their geometric applications

Benatti, Luca
2022-06-09

Abstract

In the setting of Riemannian manifolds with nonnegative Ricci curvature, we provide geometric inequalities as consequences of the Monotonicity Formulas holding along the flow of the level sets of the p-capacitary potential. The work is divided into three parts. (1) In the first part, we describe the asymptotic behaviour of the p-capactitary potential in a natural class of Riemannian manifolds. (2) The second part is devoted to the proof of our Monotonicity-Rigidity Theorems. (3) In the last part, we apply the Monotonicity Theorems to obtain geometric inequalities, focusing on the Extended Minkowski Inequality.
XXXIV
2020-2021
Matematica (29/10/12-)
Mathematics
Mazzieri, Lorenzo
no
Inglese
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/346959
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