The Patterson measure for geometrically finite groups with parabolic elements, new and old

B. Stratmann; Sanju Velani

doi:10.1112/plms/s3-71.1.197

The Patterson measure for geometrically finite groups with parabolic elements, new and old

B. Stratmann, Sanju Velani

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the Patterson measure on the limit set of a geometrically finite Kleinian group with parabolic elements. Using the d-conformality of the Patterson measure in combination with basic hyperbolic geometry we obtain a global Shadow Lemma. This macroscopic measure estimate is exploited to derive a Khintchine-type theorem, which is then used for a finer analysis of the density of the limit set in terms of Hausdorff measure.

Original language	English
Pages (from-to)	197-220
Number of pages	24
Journal	Proc. Lond. Math. Soc
Volume	s3-71
Issue number	1
DOIs	https://doi.org/10.1112/plms/s3-71.1.197
Publication status	Published - Jul 1995

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10.1112/plms/s3-71.1.197

Cite this

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title = "The Patterson measure for geometrically finite groups with parabolic elements, new and old",

abstract = "We study the Patterson measure on the limit set of a geometrically finite Kleinian group with parabolic elements. Using the d-conformality of the Patterson measure in combination with basic hyperbolic geometry we obtain a global Shadow Lemma. This macroscopic measure estimate is exploited to derive a Khintchine-type theorem, which is then used for a finer analysis of the density of the limit set in terms of Hausdorff measure. ",

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