dc.contributor.author | McMullen, Curtis T. | |
dc.date.accessioned | 2012-11-06T17:03:45Z | |
dc.date.issued | 1999 | |
dc.identifier.citation | McMullen, Curtis T. 1999. Hausdorff dimension and conformal dynamics I: Strong convergence of Kleinian groups. Journal of Differential Geometry 51(3): 471–515. | en_US |
dc.identifier.issn | 0022-040X | en_US |
dc.identifier.issn | 1945-743X | en_US |
dc.identifier.uri | http://nrs.harvard.edu/urn-3:HUL.InstRepos:9871959 | |
dc.description.abstract | This paper investigates the behavior of the Hausdorff dimensions of the limit sets \(\Lambda_n\) and \(\Lambda\) of a sequence of Kleinian groups \(\Gamma_n \rightarrow \Gamma\), where \(M = \mathbb{H}^3/\Gamma\) is geometrically finite. We show if \(\Gamma_n \rightarrow \Gamma\) strongly, then: (a) \(M_n = \mathbb{H}^3/\Gamma_n\) is geometrically finite for all \(n \gg 0\), (b) \(\Lambda_n \rightarrow \Lambda\) in the Hausdorff topology, and (c) \(H. dim(\Lambda_n) \rightarrow H. dim(\Lambda)\), if \(H. dim(\Lambda) \geq 1\). On the other hand, we give examples showing the dimension can vary discontinuously under strong limits when \(H. dim(\Lambda) < 1\). Continuity can be recovered by requiring that accidental parabolics converge radially. Similar results hold for higher-dimensional manifolds. Applications are given to quasifuchsian groups and their limits. | en_US |
dc.description.sponsorship | Mathematics | en_US |
dc.language.iso | en_US | en_US |
dc.publisher | International Press | en_US |
dc.relation.isversionof | http://www.intlpress.com/journals/JDG/archive/vol.51/issue3/3_3.pdf | en_US |
dash.license | LAA | |
dc.title | Hausdorff Dimension and Conformal Dynamics I: Strong Convergence of Kleinian Groups | en_US |
dc.type | Journal Article | en_US |
dc.description.version | Author's Original | en_US |
dc.relation.journal | Journal of Differential Geometry | en_US |
dash.depositing.author | McMullen, Curtis T. | |
dc.date.available | 2012-11-06T17:03:45Z | |
dash.contributor.affiliated | McMullen, Curtis | |