Gromov Hyperbolic Spaces and the Sharp Isoperimetric Constant
نویسنده
چکیده
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 theorems strengthen and generalize well-known results of Gromov, Papasoglu and others.
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