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math.MG2018
Quasi-doubling of self-similar measures with overlaps
Kathryn Hare, Kevin Hare, Sascha Troscheit
The Assouad and quasi-Assouad dimensions of a metric space provide information about the extreme local geometric nature of the set. The Assouad dimension of a set has a measure the…
math.CA2018
The Assouad spectrum and the quasi-Assouad dimension: a tale of two spectra
Jonathan M. Fraser, Kathryn E. Hare, Kevin G. Hare +2
We consider the Assouad spectrum, introduced by Fraser and Yu, along with a natural variant that we call the `upper Assouad spectrum'. These spectra are designed to interpolate bet…
math.MG2018
Self-conformal sets with positive Hausdorff measure
Jasmina Angelevska, Antti Käenmäki, Sascha Troscheit
We investigate the Hausdorff measure and content on a class of quasi self-similar sets that include, for example, graph-directed and sub self-similar and self-conformal sets. We sh…