Gromov hyperbolic spaces and the sharp isoperimetric constant

By S. Wenger. 2006

48 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/dda3b011e1859ff48c776df404cb34b0c049868d

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Citations in the corpus

Area Minimizing Discs in Metric Spaces (2015, background): “In fact, it follows from [56] and [58] that the corollary holds for any geodesic metric space with the sharp constant 1 4π .”
Local Currents in Metric Spaces (2011, background): “The theory of metric currents has been further developed in [8, 31, 33], and some geometric applications have been found [32, 34].”
Characterizing hyperbolic spaces and real trees (2008, result): “However, there are no reasons why 1/32 should provide a good approximation of eH and eT. On the other hand, a recent result by Wenger [ Wen08 ] on the sharp isoperimetric constant for hyperbolic spaces seems to suggest that the Euclidean plane could provide sharp bounds on the behaviour of curves an”