GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR DIFFUSION-TYPE OPERATORS ON COMPLETE RIEMANNIAN MANIFOLDS [Tesi di dottorato]
Università degli Studi di Milano, 2011-02-11
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..
diritti: info:eu-repo/semantics/openAccess
tutor: Marco Rigoli; coordinatore: Marco M. Peloso
RIGOLI, MARCO
PELOSO, MARCO MARIA
Settore MAT/03 - - Geometria


Tesi di dottorato. | Lingua: Inglese. | Paese: | BID: TD16000288