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Distribution of random Cantor sets on Tubes
- Publication Year :
- 2014
-
Abstract
- We show that there exist $(d-1)$ - Ahlfors regular compact sets $E \subset \mathbb{R}^{d}, d\geq 2$ such that for any $t< d-1$, we have \[ \sup_T \frac{\mathcal{H}^{d-1}(E\cap T)}{w(T)^t}<\infty \] where the supremum is over all tubes $T$ with width $w(T) >0$. 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.<br />Comment: 15 pages, 3 figures
- Subjects :
- Mathematics - Classical Analysis and ODEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1410.1183
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s11512-015-0219-x