Let X,Y be proper, geodesically complete CAT(-1) spaces, and let f:∂X→∂Y
be a Moebius homeomorphism. Let ϕ=ϕf:GX→GY be the associated
geodesic conjugacy.
Given 1≤p≤∞, and a family of probability measures M={μx}x∈X on GX
such that supp(μx)=T1xX for a…