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arXiv · 2610.26119

Local structure of sumsets and projections of self-affine carpets

Roope Anttila·Jonathan M. Fraser
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Abstract

We show that if $X$ and $Y$ are self-similar sets in $\mathbb{R}$ with multiplicatively independent contraction ratios, then the Assouad dimension of $X+Y$ is one. As an application, we show that for a large class of self-affine carpets, the Assouad dimension of any non-principal orthogonal projection is one. The latter result is new even for the simplest case of Bedford-McMullen carpets.

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Roope Anttila, Jonathan M. Fraser. 2026-10-19. Local structure of sumsets and projections of self-affine carpets. https://arxiv.org/abs/2610.26119

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