A Complete Realization of the Orbits of Generalized Derivatives of Quasiregular Mappings

Fletcher, Alastair; Jacob, Pratscher,

doi:10.1007/s12220-020-00439-6

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2022

2023

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Cited by 2 publications

(2 citation statements)

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“…The mean radius was used by Gutlyanskii et al [5] to construct generalized derivatives of quasiregular mappings, a topic which has been studied more recently in papers of the first named author and Wallis [4] and the authors [3]. In this paper, we will study the regularity properties of ρ f itself.…”

Section: Introductionmentioning

confidence: 99%

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On the mean radius of quasiconformal mappings

Fletcher¹,

Jacob²

2022

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We study the mean radius growth function for quasiconformal mappings. We give a new sub-class of quasiconformal mappings in R n , for n ≥ 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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Section: Introductionmentioning

confidence: 99%

“…As a generalization of the logarithmic transform to quasiregular maps, we will also use the Zorich transform introduced by the authors in [3]. This will be described in further detail below, but for a quasiconformal map f fixing 0, this is defined via a particular Zorich map Z and the functional equation…”

Section: Introductionmentioning

confidence: 99%