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Improving Kaufman's exceptional set estimate for packing dimension (1610.06745v2)

Published 21 Oct 2016 in math.CA and math.MG

Abstract: Given $0 < s < 1$, I prove that there exists a constant $\epsilon = \epsilon(s) > 0$ such that the following holds. Let $K \subset \mathbb{R}{2}$ be a Borel set with $\mathcal{H}{1}(K) > 0$, and let $E_{s}(K) \subset S{1}$ be the collection of unit vectors $e$ such that $$\dim_{\mathrm{p}} \pi_{e}(K) \leq s.$$ Then $\dim_{\mathrm{H}} E_{s}(K) \leq s - \epsilon$.

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