A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs Articles uri icon

publication date

  • June 2021

start page

  • 1

end page

  • 10


  • 154


  • 115

International Standard Serial Number (ISSN)

  • 1578-7303

Electronic International Standard Serial Number (EISSN)

  • 1579-1505


  • We study in this paper the relationship of isoperimetric inequality and hyperbolicity for
    graphs and Riemannian manifolds. We obtain a characterization of graphs and Riemannian
    manifolds (with bounded local geometry) satisfying the (Cheeger) isoperimetric inequality, in
    terms of their Gromov boundary, improving similar results from a previous work. In particular,
    we prove that having a pole is a necessary condition to have isoperimetric inequality and,
    therefore, it can be removed as hypothesis.


  • Mathematics


  • cheeger isoperimetric constant; gromov hyperbolicity; bounded local geometry; pole