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.
Titolo: | Monotonicity Formulas in Nonlinear Potential Theory and their geometric applications | |
Anno di pubblicazione: | 2022-06-09 | |
Ciclo: | XXXIV | |
Anno Accademico: | 2019-2020 | |
Struttura: | Dipartimento di Matematica | |
Corso di dottorato: | Mathematics | |
Autori Unitn: | ||
Relatore: | Mazzieri, Lorenzo | |
Tesi in cotutela: | no | |
Lingua: | Inglese | |
Appare nelle tipologie: | 08.1 Tesi di dottorato (Doctoral Thesis) |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
---|---|---|---|---|
PhD_thesis (1).pdf | Tesi di dottorato (Doctoral Thesis) | Tutti i diritti riservati (All rights reserved) | Open Access Visualizza/Apri |