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Assouad dimension

In mathematics — specifically, in fractal geometry — the Assouad dimension is a definition of fractal dimension for subsets of a metric space. It was… Expand
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Papers overview

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2019
2019
Abstract In analogy with the lower Assouad dimensions of a set, we study the lower Assouad dimensions of a measure. As with the… Expand
2017
2017
The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of the quasi… Expand
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2016
2016
In a previous paper we introduced a new `dimension spectrum', motivated by the Assouad dimension, designed to give precise… Expand
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2015
2015
The first named author is supported by a Leverhulme Trust Research Fellowship and the second named author is supported by the… Expand
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2015
2015
We consider dimensional properties of limit sets of Moran constructions satisfy- ing the finite clustering property. Just to name… Expand
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2014
2014
It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension… Expand
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Highly Cited
2013
Highly Cited
2013
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural ‘dimension pair… Expand
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2006
2006
We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The… Expand
2006
2006
In the first part of the paper we show how to relate several dimension theories (asymptotic dimension with Higson property… Expand
Highly Cited
1998
Highly Cited
1998
We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in… Expand