%0 Journal Article
%A Martínez Pérez, Álvaro
%A Rodríguez, José M.
%T On p-parabolicity of Riemannian manifolds and graphs
%D 2021
%@ 1139-1138
%@ 1988-2807
%U https://hdl.handle.net/20.500.14352/129081
%X Kanai proved that quasi-isometries between Riemannian manifolds with bounded geometry preserve many global properties, including the existence of Green’s function, i.e., non-parabolicity. However, Kanai’s hypotheses are too restrictive. Herein we prove the stability of p-parabolicity (with 1 < p < ∞) by quasi-isometries between Riemannian manifolds under weaker assumptions. Also, we obtain some results on the p-parabolicity of graphs and trees; in particular, we characterize p-parabolicity for a large class of trees.
%~