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• W3100173723 abstract "We investigate the Hausdorff measure and content on a class of quasi self-similar sets that include, for example, graph-directed and sub self-similar and self-conformal sets. We show that any Hausdorff measurable subset of such a set has comparable Hausdorff measure and Hausdorff content. In particular, this proves that graph-directed and sub self-conformal sets with positive Hausdorff measure are Ahlfors regular, irrespective of separation conditions. When restricting to self-conformal subsets of the real line with Hausdorff dimension strictly less than one, we additionally show that the weak separation condition is equivalent to Ahlfors regularity and its failure implies full Assouad dimension. In fact, we resolve a self-conformal extension of the dimension drop conjecture for self-conformal sets with positive Hausdorff measure by showing that its Hausdorff dimension falls below the expected value if and only if there are exact overlaps." @default.
• W3100173723 created "2020-11-23" @default.
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• W3100173723 date "2020-02-01" @default.
• W3100173723 modified "2023-10-14" @default.
• W3100173723 title "Self‐conformal sets with positive Hausdorff measure" @default.
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• W3100173723 doi "https://doi.org/10.1112/blms.12320" @default.
• W3100173723 hasPublicationYear "2020" @default.
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