Nonstandard uniformized conformal structures on hyperbolic manifolds

Summary The main question which the paper discusses is:Is the spaceC(M ⁿ ) of uniformized conformal structures of a finite volume (or closed) hyperbolicn-manifoldM ⁿ (or its Teichmüller space) connected or not?For the surface case (n=2) the answer is well known to be in the affirmative. By contrast, for the casen=3, we describe herein some exotic conformal structures on a closed hyperbolic 3-manifoldM which are uniformized but cannot be approximated by structures onM obtained from the distinguished conformal (=hyperbolic) structure onM by any of the presently known deformations, meaning by bendings or stampings ofM along totally geodesic submanifolds.Oblatum 17-III-1990 & 26-XI-1990This paper was written while the author was visiting Institut Mittag-Leffler, which he thanks for its hospitality. Financial support from Institut Mittag-Leffler is gratefully acknowledged. The author is thankful to Bruce Palka for his help with the English language and to Karin Lindberg for her excellent typesetting.