Filling Metric Spaces

Event time: 
Tuesday, July 30, 2019 - 10:00am
Location: 
LOM 206
Speaker: 
Alexander Nabutovsky
Speaker affiliation: 
University of Toronto
Event description: 

We prove an inequality conjectured by Larry Guth that relates the m-dimensional Hausdorff content of a compact metric space with its (m − 1)- dimensional Urysohn width.  As a corollary, we obtain new systolic inequalities that both strengthen the classical Gromov’s systolic inequality for essential Riemannian manifolds and extend this inequality to a wider class of non-simply connected manifolds.  We also present  a new version of isoperimetric inequality.  It asserts that for every positive integer m, Banach space B, compact subset of B, and a closed subset Y of X there is a filling of Y by a continuous image of X with the (m + 1)-dimensional Hausdorff content bounded in terms of the m-dimensional Hausdorff content of  Y.  Joint work with Yevgeny Liokumovich, Boris Lishak and Regina Rotman.