Graduate Groups and Dynamics Seminar
Wouter van Limbeek
UIC
Quasicircle boundaries and exotic almost-isometries
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.
Tuesday October 22, 2019 at 4:00 PM in 612 SEO