Quasisymmetric distortion spectrum
Istv\'an Prause, Stanislav Smirnov
TL;DR
This paper provides improved bounds on how quasisymmetric maps distort Hausdorff dimension, linking the bounds to the dilatation of their quasiconformal extensions and exploring the connection to harmonic measure.
Contribution
It introduces sharper bounds for Hausdorff dimension distortion under quasisymmetric maps, highlighting the relationship with quasiconformal dilatation and harmonic measure structure.
Findings
New bounds for Hausdorff dimension distortion
Connection between distortion bounds and harmonic measure
Open question on the sharpness of estimates
Abstract
We give improved bounds for the distortion of the Hausdorff dimension under quasisymmetric maps in terms of the dilatation of their quasiconformal extension. The sharpness of the estimates remains an open question and is shown to be closely related to the fine structure of harmonic measure.
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