Some analytic and geometric aspects of weighted p-Laplacian on smooth metric measure spaces.

In this paper, we generalize the well-known Kelvin–Nevanlinna–Royden criterion to check the p-hyperbolicity of the class of weighted manifolds for any p ∈ (1,∞). Besides, we introduce a new definition of a weighted cohomology and use it to derive a cohomological criterion for the weighted p-parabolicity. As a result, we acquire a global comparison principle for the weighted p-Laplacian and also receive a Liouville-type result for weighted p-harmonic functions. Moreover, we give a decay estimate for the weighted p-Laplacian on smooth metric measure spaces. Some applications to study the weighted p-parabolicity and f-minimal hypersurfaces are also given. [ABSTRACT FROM AUTHOR]