Assouad dimension influences the box and packing dimensions of orthogonal projections

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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 FRn 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.
Original languageEnglish
Pages (from-to)247–259
JournalJournal of Fractal Geometry
Volume8
Issue number3
Early online date3 May 2021
DOIs
Publication statusPublished - 2021

Keywords

  • Assouad dimension
  • Box dimension
  • Packing dimension
  • Orthogonal projection

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