Geodesic
On the asymptotics of counting functions for Ahlfors regular sets
Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 1, pp. 69-119.

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We deal with the so-called Ahlfors regular sets (also known as $s$-regular sets) in metric spaces. First we show that those sets correspond to a certain class of tree-like structures. Building on this observation we then study the following question: Under which conditions does the limit $\lim_{\varepsilon\to 0+} \varepsilon^s N(\varepsilon,K)$ exist, where $K$ is an $s$-regular set and $N(\varepsilon,K)$ is for instance the $\varepsilon$-packing number of $K$?
DOI : 10.14712/1213-7243.2022.011
Classification : 28A80, 30L99
Keywords: Ahlfors regular; $s$-regular; packing number; Minkowski measurability; renewal theory 
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Pokorný, Dušan; Rauch, Marc. On the asymptotics of counting functions for Ahlfors regular sets. Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 1, pp. 69-119. doi : 10.14712/1213-7243.2022.011. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2022.011/

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