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- W168427647 abstract "Let $Gamma$ be a discrete group of Mobius transformations acting on and preserving the unit ball in $Rdim$ (i.e. Fuchsian groups in the planar case). We will put a hyperbolic ball around each orbit point of the originand refer to their union as the {em archipelago of $Gamma$}.The main topic of this paper is the question: ``How big is the archipelago of $Gamma$?'' We will study different waysto answer various meanings of that question using concepts from potential theory such as {em minimal thinness} and {em rarefiedness} in order to give connectionsbetween the theory of discrete groups and small sets inpotential theory. One of the answers that will be given says that the critical exponent of $Gamma$ equals the Hausdorff dimension of the set on the unit sphere where the archipelago of $Gamma$ is not minimally thin. Another answer tells us that the limit set of a geometrically finiteFuchsian group $Gamma$ is the set on the boundary where the archipelago of $Gamma$ is not rarefied." @default.
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- W168427647 date "1998-01-01" @default.
- W168427647 modified "2023-10-16" @default.
- W168427647 title "Discrete groups and thin sets" @default.
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