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Yevgeny Liokumovich, RLM 10.176: Isoperimetric inequality for Hausdorff content and Guth\'s Urysohn width conjecture
Monday, February 24, 2020, 01:00pm - 02:00pm
Hausdorff content and Urysohn width are two ways of measuring the size of a metric space. Urysohn width measures how well a metric space X can be approximated by an m-dimensional polyhedral space. Hausdorff content is defined like the Hausdorff measure except that we do not take the limit with the radii of balls in the covering tending to 0. Larry Guth conjectured an inequality relating the two, which generalizes his and Gromov's results about filling Riemannian manifolds. I will talk about a proof of Guth's conjecture using an isoperimetric inequality for Hausdorff content of independent interest. This is a joint work with Boris Lishak, Alexander Nabutovsky and Regina Rotman.
Location: RLM 10.176

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