Hyperbolicity, slimness, and minsize, on average

Anna C. Gilbert, Joon-Hyeok Yim

A metric space $(X,d)$ is said to be $\delta$-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 $2\delta$. A geodesic space is $\delta$-slim if every geodesic tria…