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Monotonicity Formulas in Nonlinear Potential Theory and their geometric applications

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.

Identiferoai:union.ndltd.org:unitn.it/oai:iris.unitn.it:11572/346959
Date09 June 2022
CreatorsBenatti, Luca
ContributorsBenatti, Luca, Mazzieri, Lorenzo
PublisherUniversità degli studi di Trento, place:TRENTO
Source SetsUniversità di Trento
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/doctoralThesis
Rightsinfo:eu-repo/semantics/openAccess
Relationfirstpage:1, lastpage:145, numberofpages:145

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