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 |