PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Dmitri Burago, Anatole Katok, Aaron Brown.

Title:CONTRACTING THE BOUNDARY OF A RIEMANNIAN 2-DISC
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Yevgeniy Liokumovich, University of Toronto
Abstract:
Let D be a Riemannian 2-disc that has diameter d and length of the boundary L. M.Gromov asked the following question. Does there exist a universal constant C, say C = 1010, such that for any disc D one can contract the boundary of D to a point through curves of length ≤ C max{L, d}? S.Frankel and M.Katz gave a negative answer to this question. Then they asked if there exists a homotopy of the boundary to a point through curves of length bounded in terms of L, d and the area of the the disc A? We answer this question positively, showing that the boundary can be contracted through curves of length ≤L+200dmax{1,log( A)}. d This is a joint work with Alexander Nabutovsky and Regina Rotman.

Room Reservation Information

Room Number:MB106
Date:04 / 25 / 2012
Time:03:35pm - 05:30pm