Gromov hyperbolic spaces and the sharp isoperimetric constant
微分几何
2009-11-11 v3 群论
摘要
In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity in terms of the isoperimetric function. We prove similar results for the linear filling radius inequality. Our results strengthen and generalize theorems of Gromov, Papasoglu and others.
引用
@article{arxiv.math/0609310,
title = {Gromov hyperbolic spaces and the sharp isoperimetric constant},
author = {Stefan Wenger},
journal= {arXiv preprint arXiv:math/0609310},
year = {2009}
}
备注
Improved exposition and structure, new introduction, which includes an outline of the proof; partially new proof, not relying on asymptotic cones anymore