A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs
Differential Geometry
2020-04-07 v1
Abstract
In this paper we study the relationship of hyperbolicity and (Cheeger) isoperimetric inequality in the context of Riemannian manifolds and graphs. We characterize the hyperbolic manifolds and graphs (with bounded local geometry) verifying this 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 and, therefore, it can be removed as hypothesis.
Keywords
Cite
@article{arxiv.2004.01755,
title = {A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs},
author = {Alvaro Martinez-Perez and Jose M. Rodriguez},
journal= {arXiv preprint arXiv:2004.01755},
year = {2020}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1605.04394, arXiv:1806.04619; text overlap with arXiv:1501.02288 by other authors