# Meeting Details

For more information about this meeting, contact Svetlana Katok, Anatole Katok.

Title: Gromov hyperbolic spaces and the sharp isoperimetric constant Center for Dynamics and Geometry Seminars Stefan Wenger, Courant The classical isoperimetric inequality asserts that the area A enclosed by a closed curve of length L in the Euclidean plane satisfies 4\pi A \leq L^2 with equality exactly for circles. In this talk we will discuss the following theorem: Let X be a complete geodesic metric space. If there exists an epsilon > 0 such that every sufficiently long closed curve in X (of length L, say) bounds a 2-chain whose area A satisfies 4\pi A \leq (1-epsilon)L^2 then X is Gromov hyperbolic. This result is sharp, new even for Riemannian manifolds, and strengthens theorems of Gromov, Papasoglu, Drutu, and Bowditch. Furthermore, a similarly optimal result can be obtained for the filling radius inequality.

### Room Reservation Information

Room Number: MB106 03 / 26 / 2008 03:35pm - 04:35pm