On quasi-invariant transverse measures for the horospherical foliation of a negatively curved manifold

If M is a compact or convex-cocompact negatively curved manifold, we associate to any Gibbs measure on T-1 M a quasi-invariant transverse measure for the horospherical foliation, and prove geometrically that this measure is uniquely determined by its Radon-Nikodym cocycle. (This extends the Bowen-Marcus unique ergodicity result for this foliation.) We shall deduce from this result some equidistribution properties for the leaves of the foliation with respect to these Gibbs measures. We use it also in the study of invariant measures for horospherical foliations on regular covers of M.