Artículo

Assouad dimension influences the box and packing dimensions of orthogonal projections

Falconer, Kenneth J.; Fraser, Jonathan M.; Shmerkin, Pablo SebastianIcon
Fecha de publicación: 03/05/2021
Editorial: European Mathematical Society
Revista: Journal of Fractal Geometry
e-ISSN: 2308-1309
Idioma: Inglés
Tipo de recurso: Artículo publicado
Clasificación temática:

Resumen

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⊆Rn 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.
Palabras clave: ASSOUAD DIMENSION , BOX DIMENSION , PACKING DIMENSION , ORTHOGONAL PROJECTIONS
 
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info:eu-repo/semantics/openAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Atribución-NoComercial-SinDerivadas 2.5 Argentina (CC BY-NC-ND 2.5 AR)
Identificadores
URI: http://hdl.handle.net/11336/155243
URL: https://www.ems-ph.org/doi/10.4171/JFG/104
DOI: http://dx.doi.org/10.4171/JFG/104
URL: https://arxiv.org/abs/1911.04857
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Citación
Falconer, Kenneth J.; Fraser, Jonathan M.; Shmerkin, Pablo Sebastian; Assouad dimension influences the box and packing dimensions of orthogonal projections; European Mathematical Society; Journal of Fractal Geometry; 8; 3; 3-5-2021; 247–259
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