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On the Assouad dimension of projections (1902.04993v3)
Published 13 Feb 2019 in math.CA and math.MG
Abstract: Let $F \subset \mathbb{R}{2}$, and let $\dim_{\mathrm{A}}$ stand for Assouad dimension. I prove that $\dim_{\mathrm{A}} \pi_{e}(F) \geq \min{\dim_{\mathrm{A}} F,1}$ for all $e \in S{1}$ outside of a set of Hausdorff dimension zero. This is a strong variant of Marstrand's projection theorem for Assouad dimension, whose analogue is not true for other common notions of fractal dimension, such as Hausdorff or packing dimension.