We study the appropriate versions of parabolicity stochastic completeness and related Liouville properties for a general class of operators which include the -Laplace operator, and the non linear singular operators in non-diagonal form considered by J. Serrin and collaborators.
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Stefano Pigola, Marco Rigoli, Alberto G. Setti, Some non-linear function theoretic properties of Riemannian manifolds. Rev. Mat. Iberoam. 22 (2006), no. 3, pp. 801–831DOI 10.4171/RMI/474