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math.MG2026
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…
math.MG2025
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…
math.MG2025
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…