46 citations · 268 across the 58 of their papers we have counts for
9 papers · 1 filter
Regularity versus smoothness of measures
Jonathan M. Fraser, Sascha Troscheit
The Assouad and lower dimensions and dimension spectra quantify the regularity of a measure by considering the relative measure of concentric balls. On the other hand, one can quan…
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…
The box dimensions of exceptional self-affine sets in
Jonathan M. Fraser, Natalia Jurga
We study the box dimensions of self-affine sets in which are generated by a finite collection of generalised permutation matrices. We obtain bounds for the dimension…
Projection theorems for intermediate dimensions
Stuart A. Burrell, Kenneth J. Falconer, Jonathan M. Fraser
Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions m…
Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images
Ábel Farkas, Jonathan M. Fraser, Erez Nesharim +1
We consider Schmidt's game on the space of compact subsets of a given metric space equipped with the Hausdorff metric, and the space of continuous functions equipped with the supre…
On Hölder solutions to the spiral winding problem
Jonathan M. Fraser
The winding problem concerns understanding the regularity of functions which map a line segment onto a spiral. This problem has relevance in fluid dynamics and conformal welding th…
Approximate arithmetic structure in large sets of integers
Jonathan M. Fraser, Han Yu
We prove that if a set is `large' in the sense of Erdős, then it approximates arbitrarily long arithmetic progressions in a strong quantitative sense. More specifically, expressing…
Interpolating between dimensions
Jonathan M. Fraser
Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to c…