92 citations · 502 across the 56 of their papers we have counts for
4 papers · 1 filter
On sets containing a unit distance in every direction
Pablo Shmerkin, Han Yu
We investigate the box dimensions of compact sets in that contain a unit distance in every direction (such sets may have zero Hausdorff dimension). Among other resul…
Assouad dimension influences the box and packing dimensions of orthogonal projections
Kenneth J. Falconer, Jonathan M. Fraser, Pablo Shmerkin
We present several applications of the Assouad dimension, and the related quasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions of orthogonal projections…
Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
Jonathan M. Fraser, Pablo Shmerkin, Alexia Yavicoli
We provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real line which avoid -approximations of arithmetic progressions. Some of…
dimensions of self-similar measures, and applications: a survey
Pablo Shmerkin
We present a self-contained proof of a formula for the dimensions of self-similar measures on the real line under exponential separation (up to the proof of an inverse theore…