Gaps in the exponent spectrum of subgroups of discrete quasiconformal groups

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概要

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• Let G be a discrete quasiconformal group preserving B3 whose limit set Λ(G) is purely conical and all of ∂B3. Let Ĝ be a non-elementary normal subgroup of G: we show that there exists a set $¥mathcal{A}$ of full measure in Λ(G) so that $¥mathcal{A}$, regarded as a subset of Λ (Ĝ), has "fat horospherical" dynamics relative to Ĝ. As an application we will bound from below the exponent of convergence of Ĝ in terms of the Hausdorff dimension of $¥mathcal{A}$.

• 国立大学法人 東京工業大学大学院理工学研究科数学専攻の論文

著者

• Bonfert-Taylor Petra

  Wesleyan University

• Falk Kurt

  National University of Ireland at Maynooth

• Taylor Edward

  Wesleyan University

関連論文

• Gaps in the exponent spectrum of subgroups of discrete quasiconformal groups

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