Assouad-type dimensions are a family of dimensions which capture the “coarsest” scaling properties of a set. This area has been very active recently, with a large amount of interest in this field from various points of view, such as conformal geometry, embedding theory, and fractal geometry.
In this area, I have proven classification results for Assouad spectra and studied the Assouad dimension of overlapping self-affine carpets in my joint paper with Jonathan Fraser.
- Assouad-type dimensions of overlapping self-affine sets
With: Jonathan M. Fraser Journal: Preprint (submitted) Links: pdfarxiv
- Attainable forms of Assouad spectra
Journal: Indiana Univ. Math. J. (to appear) Links: pdfarxiv