Hyperbolicity, slimness, and minsize, on average

Anna C. Gilbert, Joon-Hyeok Yim

A metric space $(X,d)$ is said to be $\hat{I}´$-hyperbolic if $d(x,y)+d(z,w)$ is at most $\max (d(x,z)+d(y,w),d(x,w)+d(y,z))$ by $2\hat{I}´$. A geodesic space is $\hat{I}´$-slim if every geodesic t…