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

Title: | Gromov hyperbolic spaces and the sharp isoperimetric constant |

Seminar: | Center for Dynamics and Geometry Seminars |

Speaker: | Stefan Wenger, Courant |

Abstract: |

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 |

Date: | 03 / 26 / 2008 |

Time: | 03:35pm - 04:35pm |