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arXiv · 2201.03037

On the mean radius of quasiconformal mappings

Alastair Fletcher·Jacob Pratscher
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Abstract

We study the mean radius growth function for quasiconformal mappings. We give a new sub-class of quasiconformal mappings in $\mathbb{R}^n$, for $n\geq 2$, called bounded integrable parameterization mappings, or BIP maps for short. These have the property that the restriction of the Zorich transform to each slice has uniformly bounded derivative in $L^{n/(n-1)}$. For BIP maps, the logarithmic transform of the mean radius function is bi-Lipschitz. We then apply our result to BIP maps with simple infinitesimal spaces to show that the asymptotic representation is indeed quasiconformal by showing that its Zorich transform is a bi-Lipschitz map.

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Alastair Fletcher, Jacob Pratscher. 2022-01-09. On the mean radius of quasiconformal mappings. https://arxiv.org/abs/2201.03037

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