Assouad dimension influences the box and packing dimensions of orthogonal projections
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We present several applications of the Assouad dimension, and the related quasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions of orthogonal projections of sets. For example, we show that if the (quasi-)Assouad dimension of F ⊆ R n is no greater than m, then the box and packing dimensions of F are preserved under orthogonal projections onto almost all m-dimensional subspaces. We also show that the threshold m for the (quasi-)Assouad dimension is sharp, and bound the dimension of the exceptional set of projections strictly away from the dimension of the Grassmannian.
Falconer , K J , Fraser , J & Shmerkin , P 2021 , ' Assouad dimension influences the box and packing dimensions of orthogonal projections ' , Journal of Fractal Geometry . https://doi.org/10.4171/jfg/104
Journal of Fractal Geometry
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DescriptionFunding: UK EPSRC Standard Grant (EP/R015104/1) (KJF and JMF). Leverhulme Trust Research Project Grant (RPG-2019-034) (JMF). Royal Society International Exchange grant IES\R1\191195 (KJF and PS). ProjectPICT 2015-3675 (ANPCyT) (PS).
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