Analysis Seminar

Sascha Troscheit, Department of Pure Mathematics, University of Waterloo

"Quasi self-similarity and the dimension drop conjecture for self-conformal sets"

The family of quasi self-similar sets is a rich collection that encompasses many Julia sets in complex dynamics. In this talk we will investigate the Hausdorff measure of these sets and show that positive Hausdorff measure is equivalent to Ahlfors regularity. We will further relate this to the dimension drop conjecture and apply our work to confirm the conjecture for self-conformal sets with positive Hausdorff measure.

MC 5417