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Mostow rigidity of rank 1 discrete groups with ergodic Bowen-Margulis measure. (English) Zbl 0853.58076
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)), 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.
Reviewer: R.Cowen (Gaborone)

37A99 Ergodic theory
57S25 Groups acting on specific manifolds
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