Bending parameterization of one-sided degenerate Kleinian surface groups

Abstract

It was recently proved that quasi-Fuchsian manifolds are uniquely determined by their bending laminations. This paper concerns a similar result for certain non-quasi-Fuchsian manifolds~: those obtained by degenerating one end but not the other, i.e. those appearing in boundaries of Bers slices. More precisely, we show that such hyperbolic manifolds are uniquely determined by the end structure of the degenerated end and the bending lamination of the other. The end structure consists of the parabolic locus, which is a multicurve, together with ending laminations or conformal structures on each components of its complement.

arXiv comment14 pages, 1 figure, comments are welcome! v3 : corrections and clarity improvements. The strategy of Section 3 (continuity) was changed and shortened. Titled changed