Mostow rigidity of rank 1 discrete groups with ergodic Bowen-Margulis measure (Q1914833)

This paper is a sequel of the author's papers `The ergodic theory of discrete isometry groups on manifolds of variable negative curvature'. Trans. Am. Math. Soc. (to appear) and Ann. Math., II. Ser. 143, No. 2, 331-355 (1996; Zbl 0843.22019). In `Seminar on conformal and hyperbolic geometry; Publ. Math. IHES (preprint, March (1983)), \textit{D. Sullivan} asked whether his rigidity result can be extended to discrete subgroups in other semisimple Lie groups. The author answers this question for the (remaining) rank 1 case. Specifically, an extension of Mostow rigidity is proved for discrete isometry groups of the complex, quaternionic or Cayley hyperbolic spaces of infinite covolume.