8 papers
Quasiconformal distortion of the lower dimension and applications
Efstathios Konstantinos Chrontsios Garitsis, Jeremy T. Tyson
We study the distortion of the lower dimension and lower spectrum of sets under quasiconformal mappings. As an application, we verify weighted Hardy--Sobolev inequalities in Euclid…
Quasiconformal and Sobolev distortion of dimension
Jeremy T. Tyson
We review a selection of the literature on the distortion of metric notions of dimension under quasiconformal, quasisymmetric, and Sobolev mappings. Our story begins with Gehring's…
Analytic and quasiregular distortion of Nagata dimension
Manisha Garg, Jeremy T. Tyson
We study how analytic functions, and more generally quasiregular mappings, distort Nagata dimension. Quasiconformal mappings of domains preserve the Nagata dimension of compact sub…
The Heinonen-Semmes problems after thirty years
Guy C. David, Pekka Pankka, Jeremy T. Tyson
We survey the current status of the questions posed by Juha Heinonen and Stephen Semmes in `Thirty-three yes or no questions about mappings, measures, and metrics' (Conformal Geome…
Metric spaces with small rough angles and the rectifiability of rough self-contracting curves
Estibalitz Durand-Cartagena, Jeremy T. Tyson
The small rough angle ($\mbox{SRA}$) condition, introduced by Zolotov in arXiv:1804.00234, captures the idea that all angles formed by triples of points in a metric space are small…
On the H-type deviation of step two Carnot groups
Luca Nalon, Jeremy T. Tyson
The H-type deviation, , of a step two Carnot group quantifies the extent to which deviates from the geometrically and algebraically trac…
On the Assouad spectrum of Hölder and Sobolev graphs
Efstathios Konstantinos Chrontsios Garitsis, Jeremy T. Tyson
We provide upper bounds for the Assouad spectrum of the graph of a real-valued Hölder or Sobolev function defined on an interval …
Quasiconformal distortion of the Assouad spectrum and classification of polynomial spirals
Efstathios Konstantinos Chrontsios Garitsis, Jeremy T. Tyson
We investigate the distortion of Assouad dimension and the Assouad spectrum under Euclidean quasiconformal maps. Our results complement existing conclusions for Hausdorff and box-c…