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Every Planar Set has a Conformally Removable Subset with the Same Hausdorff Dimension

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arxiv 1912.00301 v1 pith:BTNEI7PP submitted 2019-12-01 math.CV

classification math.CV
keywords subsetconformallydimensionhausdorffremovablesamealwayscompact
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abstract

In this paper we show that given any compact set $E \subset \hat{\mathbb{C}}$, we can always find a conformally removable subset with the same Hausdorff dimension as $E$.

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