Wouter van Limbeek : Quasicircle boundaries and exotic almost-isometries

Posted by Wouter Van Limbeek , part of the Graduate Groups and Dynamics Seminar.

At

Oct. 22, 2019, 4 p.m.

In

612 SEO

Abstract

For negatively curved surfaces, we study visual metrics on the boundary at infinity of their universal covers. We prove that the visual metric is classified up to bi-Lipschitz equivalence by its Hausdorff dimension, and we use this to construct many non-isometric negatively curved surfaces whose universal covers are almost-isometric (= quasi-isometric with multiplicative constant 1). As an application, we answer a question Alex posed in the first seminar this semester (due to him? Or Hamenstaedt?): Are there negatively curved metrics on a surface such that they are not isometric in any finite cover but almost-isometric on the universal cover? Joint work with Jean-François Lafont and Ben Schmidt.