GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR DIFFUSION-TYPE OPERATORS ON COMPLETE RIEMANNIAN MANIFOLDS
Tesi di Dottorato
Data di Pubblicazione:
2011
Citazione:
GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR DIFFUSION-TYPE OPERATORS ON COMPLETE RIEMANNIAN MANIFOLDS / P. Mastrolia ; tutor: Marco Rigoli; coordinatore: Marco M. Peloso. Universita' degli Studi di Milano, 2011 Feb 11. 23. ciclo, Anno Accademico 2010. [10.13130/mastrolia-paolo_phd2011-02-11].
Abstract:
The aim of this work is twofold. The first main concern, the analytical one, is to study, using the method of gradient estimates, various Liouville-type theorems which are extensions of the classical Liouville Theorem for harmonic functions. We generalize the setting - from the Euclidean space to complete Riemannian manifolds - and the relevant operator - from the Laplacian to a general diffusion operator - and we also consider ``relaxed'' boundedness conditions (such as non-negativity, controlled growth and so on).
The second main concern is geometrical, and is deeply related to the first: we prove some triviality results for Einstein warped products and quasi-Einstein manifolds studying a specific Poisson equation for a particular, and geometrically relevant, diffusion operator.
Tipologia IRIS:
Tesi di dottorato
Elenco autori:
P. Mastrolia
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