Special Colloquium
Stefan Wenger
Courant Institute of Mathematical Sciences
Isoperimetric inequalities and the large scale geometry of metric spaces
Abstract: Isoperimetric inequalities appear in many branches of mathematics and play an important role notably in geometry, analysis and geometric group theory. The purpose of this talk is to discuss results which exhibit relationships between the growth of isoperimetric functions and the asymptotic geometry of Riemannian manifolds (and more generally of singular spaces). An optimal result in this direction shows that a geodesic metric space cannot have a quadratic isoperimetric inequality for (sufficiently long) curves with isoperimetric constant strictly smaller than 1/(4pi), unless it is Gromov hyperbolic. Gromov hyperbolic spaces should be thought of as spaces of negative curvature on a large scale. Our result is optimal (with Euclidean space as a borderline case) and new even for Riemannian manifolds. It generalizes and strengthens well-known results of Gromov, Bowditch, Drutu and Papasoglu.
There will be a meet and greet right after the talk in SEO 300. Coffee, tea, & cookies will be provided.
Friday January 11, 2008 at 3:00 PM in SEO 636