Abstract
We show that there exist -Ahlfors regular compact sets , such that for any , we have where the supremum is over all tubes with width . This settles a question of T. Orponen. The sets we construct are random Cantor sets, and the method combines geometric and probabilistic estimates on the intersections of these random Cantor sets with affine subspaces.
Funding Statement
The author was supported by the Vilho, Yrjö, and Kalle Väisälä foundation.
Citation
Changhao Chen. "Distribution of random Cantor sets on tubes." Ark. Mat. 54 (1) 39 - 54, April 2016. https://doi.org/10.1007/s11512-015-0219-x
Information