Hausdorff dimension of non-conical limit sets

Kapovich, Michael; Liu, Beibei

doi:10.1090/tran/8166

Hausdorff dimension of non-conical limit sets
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Trans. Amer. Math. Soc. 373 (2020), 7207-7224 Request permission

Abstract:

Geometrically infinite Kleinian groups have non-conical limit sets with the cardinality of the continuum. In this paper, we construct a geometrically infinite Fuchsian group such that the Hausdorff dimension of the non-conical limit set equals zero. For finitely generated, geometrically infinite Kleinian groups, we prove that the Hausdorff dimension of the non-conical limit set is positive.

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