On p-parabolicity of Riemannian manifolds and graphs Articles uri icon

publication date

  • January 2022

start page

  • 179

end page

  • 198


  • 1


  • 35

International Standard Serial Number (ISSN)

  • 1139-1138

Electronic International Standard Serial Number (EISSN)

  • 1988-2807


  • 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
    ) 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.


  • Mathematics


  • bounded local geometry; p-parabolicity; parabolicity; quasi-isometries