Characterizations of Higher Rank Hyperbolicity

A striking feature of Gromov hyperbolicity is that it can be characterized in many ways. With mild assumptions on the underlying metric space, equivalent properties include thin triangle conditions, the stability of quasi-geodesics, a linear isoperimetric filling inequality, and a sub-quadratic isoperimetric inequality.
We present an analogous list of six equivalent conditions in the context of generalized non-positive curvature and higher asymptotic rank, complementing results of Wenger and Kleiner-Lang.
If time permits we will discuss applications to minimal simplices in proper CAT(0) spaces. Joint work with Urs Lang.