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Some non-linear function theoretic properties of Riemannian manifolds.

Stefano Pigola, Marco Rigoli, Alberto G. Setti (2006)

Revista Matemática Iberoamericana

We study the appropriate versions of parabolicity stochastic completeness and related Liouville properties for a general class of operators which include the p-Laplace operator, and the non linear singular operators in non-diagonal form considered by J. Serrin and collaborators.

Some remarks on almost-positivity of ψ do 's

Cesare Parenti, Alberto Parmeggiani (1998)

Bollettino dell'Unione Matematica Italiana

Per una classe di operatori pseudodifferenziali a caratteristiche multiple vengono date condizioni necessarie e sufficienti per la validità di stime dal basso «ottimali»

Some remarks on the weak maximum principle.

Marco Rigoli, Maura Salvatori, Marco Vignati (2005)

Revista Matemática Iberoamericana

We obtain a maximum principle at infinity for solutions of a class of nonlinear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumptions of volume growth conditions. In the case of the Laplace-Beltrami operator we relate our results to stochastic completeness and parabolicity of the manifold.

Special invariant operators I

Jarolím Bureš (1996)

Commentationes Mathematicae Universitatis Carolinae

The aim of the first part of a series of papers is to give a description of invariant differential operators on manifolds with an almost Hermitian symmetric structure of the type G / B which are defined on bundles associated to the reducible but undecomposable representation of the parabolic subgroup B of the Lie group G . One example of an operator of this type is the Penrose’s local twistor transport. In this part general theory is presented, and conformally invariant operators are studied in more...

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