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Assouad dimension influences the box and packing dimensions of orthogonal projections

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Falconer_2021_Assouad_dimension_influences_JFG_8_3_247_CCBY.pdf (165.2Kb)
Date
2021
Author
Falconer, Kenneth John
Fraser, Jonathan
Shmerkin, Pablo
Funder
EPSRC
The Leverhulme Trust
Grant ID
EP/R015104/1
RPG-2019-034
Keywords
Assouad dimension
Box dimension
Packing dimension
Orthogonal projection
QA Mathematics
T-NDAS
Metadata
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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 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.
Citation
Falconer , K J , Fraser , J & Shmerkin , P 2021 , ' Assouad dimension influences the box and packing dimensions of orthogonal projections ' , Journal of Fractal Geometry , vol. 8 , no. 3 , pp. 247–259 . https://doi.org/10.4171/jfg/104
Publication
Journal of Fractal Geometry
Status
Peer reviewed
DOI
https://doi.org/10.4171/jfg/104
ISSN
2308-1309
Type
Journal article
Rights
Copyright © 2021 European Mathematical Society Published by EMS Press This work is licensed under a CC BY 4.0 license.
Description
Funding: 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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  • University of St Andrews Research
URL
https://arxiv.org/abs/1911.04857
https://ems.press/journals/jfg/articles/985977
URI
http://hdl.handle.net/10023/19646

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