The Klein, Hilbert and Poincaré metrics of a domain

摘要

Let D be a bounded strictly convex domain in Euclidean n-space equipped with its Hilbert metric h(x,y). It is shown that as the points x and y of D approach distinct points on the boundary of D, for any a in D the sum h(x,a)+h(a,y) is asymptotic to h(x,y).