Compactification of a diagonal action on the product of CAT(-1) spaces
  Let $X$ be a proper, non-compact CAT(-1) space, and $\Gamma$ a discrete cocompact subgroup of the isometries of $X$. We compactify the diagonal action of $\Gamma$ on $X \times X$ considering a domain of the horofunction boundary with respect to the maximum metric. 
Teresa Garc\'ia
math.MG