Abstract:Let (M, g) be a complete non-compact Riemannian manifold together with a function e h , which weights the Hausdorff measures associated to the Riemannian metric. In this work we assume lower or upper radial bounds on some weighted or unweighted curvatures of M to deduce comparisons for the weighted isoperimetric quotient and the weighted capacity of metric balls in M centered at a point o ∈ M . As a consequence, we obtain parabolicity and hyperbolicity criteria for weighted manifolds generalizing previous ones… Show more
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