Assouad dimension influences the box and packing dimensions of orthogonal projections

  • Kenneth J. Falconer

    University of St Andrews, UK
  • Jonathan M. Fraser

    University of St Andrews, UK
  • Pablo Shmerkin

    Torcuato Di Tella University, Buenos Aires, Argentina
Assouad dimension influences the box and packing dimensions of orthogonal projections cover
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Abstract

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 is no greater than , then the box and packing dimensions of are preserved under orthogonal projections onto almost all -dimensional subspaces. We also show that the threshold 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.

Cite this article

Kenneth J. Falconer, Jonathan M. Fraser, Pablo Shmerkin, Assouad dimension influences the box and packing dimensions of orthogonal projections. J. Fractal Geom. 8 (2021), no. 3, pp. 247–259

DOI 10.4171/JFG/104