Gromov Hyperbolic Spaces and Optimal Constants for Isoperimetric and Filling Radius Inequalities
نویسنده
چکیده
A. In this article we exhibit the optimal (i.e. largest) constants for the quadratic isoperimetric and the linear filling radius inequality which ensure that a geodesic metric space X is Gromov hyperbolic. Our results show that the Euclidean plane is a borderline case for the isoperimetric inequality. Furthermore, by only requiring the existence of isoperimetric fillings in L∞(X) satisfying the appropriate area bounds we obtain the same optimal results for spaces X in which Lipschitz loops merely admit coarse fillings. In particular, our results apply to Cayley graphs of finitely presented groups with quadratic Dehn function. Finally, we use filling techniques to prove purely metric characterizations of real trees and Gromov hyperbolic spaces.
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