Abstract: We investigate the Hausdorff measure and content on a class of quasi self-similar sets that include self-conformal sets such as many Julia sets in complex dynamics. We show that any Hausdorff measurable subset of such sets has uniformly comparable Hausdorff measure and Hausdorff content. This result relates to other notions of regularity such as Ahlfors regularity and we will explore its link to the dimension drop conjecture. In particular, we use our results to resolve the self-conformal analogue of the dimension drop conjecture for subsets of the line with positive Hausdorff measure. (Joint with Antti Käenmäki)
Self-conformal sets with positive Hausdorff measure
25.01.2019 15:15 - 16:15
Organiser:
H. Bruin, P. Balint
Location: