Bending parameterization of one-sided degenerated 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.
Cite
@article{arxiv.2504.19891,
title = {Bending parameterization of one-sided degenerated Kleinian surface groups},
author = {Bruno Dular},
journal= {arXiv preprint arXiv:2504.19891},
year = {2025}
}
Comments
14 pages, 1 figure, comments are welcome! v2 : corrected gap in proof of Proposition 4.3, updated reference to recent preprint by C. Lecuire (arXiv:2510.07087)