Gromov hyperbolic spaces and the sharp isoperimetric constant

Details Gromov hyperbolic spaces and the sharp isoperimetric constant Gromov hyperbolic spaces and the sharp isoperimetric constant

2006-09-11

arxiv.org/abs/math/0609310v3

Mathematics

Differential Geometry

Improved exposition and structure, new introduction, which includes an outline of the proof; partially new proof, not relying

Scientific paper

10.1007/s00222-007-0084-8

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.

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