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arXiv · 2109.10087

A note on the Hausdorff dimension of uniformly non flat sets with plenty of big projections

Michele Villa
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Abstract

Using a recent result of Orponen (Invent. math. '21), we show that sets with plenty of big projections (PBP) admit an Analyst's Travelling Salesman Theorem. We then show that sets with PBP which are uniformly non-flat (or wiggly) have large Hausdorff dimension. We also obtain a corollary on analytic/Lipschitz harmonic capacities.

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Michele Villa. 2021-09-21. A note on the Hausdorff dimension of uniformly non flat sets with plenty of big projections. https://arxiv.org/abs/2109.10087

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