Abstract
Susskind’s conjecture states that for subgroups \(\Phi \) and \(\Theta \) of a Kleinian group \(\Gamma \) acting on \({\mathbb H}^n\), we have that \(\Lambda _c(\Phi )\cap \Lambda _c (\Theta )\subset \Lambda (\Phi \cap \Theta )\), where \(\Lambda _c(\Phi )\) is the set of conical limit points of \(\Phi \) and \(\Lambda (\Phi )\) is the limit set of \(\Phi \). We show that Susskind’s conjecture largely holds for purely loxodromic Kleinian groups and we present two examples to illustrate that Susskind’s conjecture is nearly optimal.
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Communicated by Gaven Martin.
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Anderson, J.W. Limit Set Intersection Theorems for Kleinian Groups and a Conjecture of Susskind. Comput. Methods Funct. Theory 14, 453–464 (2014). https://doi.org/10.1007/s40315-014-0078-7
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DOI: https://doi.org/10.1007/s40315-014-0078-7