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The Patterson Measure for Geometrically Finite Groups with Parabolic Elements, New and Old
Author(s) -
Stratmann B.,
Velani S. L.
Publication year - 1995
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-71.1.197
Subject(s) - mathematics , kleinian group , measure (data warehouse) , hausdorff measure , lemma (botany) , limit (mathematics) , mathematical analysis , σ finite measure , pure mathematics , hausdorff dimension , computer science , ecology , poaceae , database , biology
We study the Patterson measure on the limit set of a geometrically finite Kleinian group with parabolic elements. Using the δ‐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.