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Hausdorff dimension of restricted Kakeya sets

math.CA · 2025-05-09 · conditional · novelty 7.0

For a Kakeya set in R^n whose line-segment midpoints lie in a set A of packing dimension at most s, the Hausdorff dimension is at least n-s, with bush-argument improvements, e.g. max{19/5-3s/5, 4-s} for n=4.

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  • Hausdorff dimension of restricted Kakeya sets math.CA · 2025-05-09 · conditional · none · ref 3

    For a Kakeya set in R^n whose line-segment midpoints lie in a set A of packing dimension at most s, the Hausdorff dimension is at least n-s, with bush-argument improvements, e.g. max{19/5-3s/5, 4-s} for n=4.