学术报告（周青山 11.20）

摘要：I

n this lecture series, I will introduce the connection between Gromov hyperbolic category and uniform space category.

We will start with Gromov hyperbolic geometry and then introduce a conformal density via Busemann function, from which one can obtain a uniformization theorem for Gromov hyperbolic spaces. This generalizes the work of Bonk,Heinonen and Koskela.

Then we introduce Gromov hyperbolization of metric spaces. We will focus on hyperbolic fillings of compact spaces and hyperbolic type metrics defined on non-complete spaces.

The second half of the series will show that there is a one-to-one correspondence between

the quasi-isometry classes of proper geodesic Gromov hyperbolic spaces that are roughly starlike with respect to the points at the boundaries of infinity and the quasi-similarity classes of unbounded locally compact uniform spaces. We will explain its relations to Teichmuller displacement theorem, Heinonen-Nakki-Vaisala theorem, QS/QC structure from local to global.