Holomorphic motions, dimension, area and quasiconformal mappings
Complex Variables
2023-04-10 v2 Dynamical Systems
Abstract
We describe the variation of the Minkowski, packing and Hausdorff dimensions of a set moving under a holomorphic motion, as well as the variation of its area. Our method provides a new, unified approach to various celebrated theorems about quasiconformal mappings, including the work of Astala on the distortion of area and dimension under quasiconformal mappings and the work of Smirnov on the dimension of quasicircles.
Keywords
Cite
@article{arxiv.2302.07743,
title = {Holomorphic motions, dimension, area and quasiconformal mappings},
author = {Aidan Fuhrer and Thomas Ransford and Malik Younsi},
journal= {arXiv preprint arXiv:2302.07743},
year = {2023}
}
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33 pages