Title
Quasihyperbolic domains are CAT(2)
Abstract
The quasihyperbolic metric on Euclidean domains was introduced by Gehring and Palka in 1976. Shortly after, Gehring and Osgood used the quasihyperbolic metric to classify uniform domains. Since then, the metric has found numerous applications in Sobolev analysis and on uniformization problems. Nevertheless, the local geometry of quasihyperbolic metrics is not well-understood. This motivated Väisälä to propose several conjectures in 2009 concerning the local structure of quasihyperbolic metrics/geodesics.
We positively resolved Väisälä's conjectures in a recent joint work with Abhishek Pandey (JYU). To achieve this, we proved the sharp result that any Euclidean domain equipped with the quasihyperbolic metric is CAT(2). During the talk, we will introduce the setting and some of the results.
