Potenziali di Evans su varietà paraboliche
This is my master thesis. Unfortunately it is written in Italian, but maybe somebody will find it helpful when it comes to Evans Potentials
math.DG↗
arXiv subjects
Daniele Valtorta
Publications and source records attributed to Daniele Valtorta.
On the equivalence of stochastic completeness, Liouville and Khas'minskii condition in linear and nonlinear setting
Set in Riemannian enviroment, the aim of this paper is to present and discuss some equivalent characterizations of the Liouville property relative to special operators, in some sense modeled after the p-Laplacian with potential. In particular, we discuss the equivalence between the Lioville property and the Khas'minskii condition, i.e. the existence of an exhaustion functions which is also a supersolution for the operator outside a compact set. This generalizes a previous result obtained by one of the authors and answers to a question in "Aspects of potential theory, linear and nonlinear" by Pigola, Rigoli and Setti.
math.AP↗
Stokes' theorem, volume growth and parabolicity
We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced.
math.DG↗
Reverse Khas'minskii condition
The aim of this paper is to present and discuss some equivalent characterizations of p-parabolicity in terms of existence of special exhaustion functions. In particular, Khas'minskii in [K] proved that if there exists a 2-superharmonic function k defined outside a compact set such that $\lim_{x\to \infty} k(x)=\infty$, then R is 2-parabolic, and Sario and Nakai in [SN] were able to improve this result by showing that R is 2-parabolic if and only if there exists an Evans potential, i.e. a 2-harmonic function $E:R\setminus K \to \R^+$ with $\lim_{x\to \infty} \E(x)=\infty$. In this paper, we will prove a reverse Khas'minskii condition valid for any p>1 and discuss the existence of Evans potentials in the nonlinear case.
math.DG↗