Improving Kaufman's exceptional set estimate for packing dimension

2016/10/21 by Tuomas Orponen, Orponen, Tuomas · 1 citation
Mathematics · #Analytic and geometric function theory #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #math.CA #math.MG

paper · pdf · doi:10.48550/arxiv.1610.06745

22 pages. v2: Significantly improved main result; changed title accordingly

arxiv created 2016/11/13 · arxiv updated 2016/11/15

Abstract

Given 0 < s < 1, I prove that there exists a constant ε= ε(s) > 0 such that the following holds. Let K ⊂ ℝ² be a Borel set with H¹(K) > 0, and let E_s(K) ⊂ S¹ be the collection of unit vectors e such that dim_p π_e(K) ≤ s. Then dim_H E_s(K) ≤ s - ε.

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• Projections in vector spaces over finite fields

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