Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T15:18:15.328Z Has data issue: false hasContentIssue false

On the Stable Basin Theorem

Published online by Cambridge University Press:  20 November 2018

John R. Parker*
Affiliation:
Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, England, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The stable basin theorem was introduced by Basmajian and Miner as a key step in their necessary condition for the discreteness of a non-elementary group of complex hyperbolic isometries. In this paper we improve several of Basmajian and Miner’s key estimates and so give a substantial improvement on the main inequality in the stable basin theorem.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Basmajian, A. & Miner, R., Discrete subgroups of complex hyperbolic motions. Invent.Math. 131 (1998), 85136.Google Scholar
[2] Goldman, W. M., Complex Hyperbolic Geometry. Oxford University Press, 1999.Google Scholar
[3] Jiang, Y., Kamiya, S. & Parker, J. R., Jørgensen's inequality for complex hyperbolic space. Geom. Dedicata 97 (2003), 5580.Google Scholar
[4] Jørgensen, T., On discrete groups of Möbius transformations. Amer. J. Math. 98 (1976), 739749.Google Scholar
[5] Kamiya, S., On discrete subgroups of PU(1, 2; C) with Heisenberg translations. J. LondonMath. Soc. 62 (2000), 827842.Google Scholar
[6] Kamiya, S. & Parker, J. R., On discrete subgroups of PU(1, 2; C) with Heisenberg translations II. Rev. RoumaineMath. Pures Appl. 47 (2002), 687693.Google Scholar
[7] Parker, J. R., Uniform discreteness and Heisenberg translations. Math. Z. 225 (1997), 485505.Google Scholar