PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Mari Royer, Yakov Pesin, Anatole Katok, Svetlana Katok, Dmitri Burago.

Title:Compactness for manifolds with bounded volume and diameter (THIS TALK WILL TAKE PLACE IN THE SYNERGISTIC ROOM)
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Stefan Wenger, University of Illinois at Chicago
Abstract:
Gromov's compactness theorem for metric spaces asserts that every uniformly compact sequence of metric spaces has a subsequence which converges in the Gromov-Hausdorff sense to a compact metric space. This theorem has been of great importance in Riemannian an metric geometry, but also other fields. I will show in this talk that if one replaces the Hausdorff distance appearing in Gromov's theorem by the filling volume or flat distance then every sequence of oriented k-dimensional Riemannian manifolds with a uniform bound on diameter and volume has a subsequence which converges in this new distance to a countably k-rectifiable metric space. In general, such a sequence does not meet the conditions of Gromov's theorem and does not have a subsequence which converges with respect to the Gromov-Hausdorff distance. The new distance mentioned above was first introduced and studied by Christina Sormani and myself. In the talk, which will be self-contained, I will explain the basic properties of this distance and illustrate it by examples. >

Room Reservation Information

Room Number:MB106
Date:01 / 26 / 2009
Time:04:00pm - 05:00pm