Parametric Representations of Quasiconformal Mappings
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DOI: 10.1007/s10473-020-0616-5
Abstract: In this article, we first give two simple examples to illustrate that two types of parametric representation of the family of Σ0 have some gaps. Then we also find that the area derivative formula (1.6),… read more here.
Keywords: parametric representations; quasiconformal mappings; representations quasiconformal;
Prime ends in the Heisenberg group H_1 and the boundary behavior of quasiconformal mappings
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DOI: 10.5186/aasfm.2018.4342
Abstract: We investigate prime ends in the Heisenberg group $\mathbb{H}_{1}$ extending N\"akki's construction for collared domains in Euclidean spaces. The corresponding class of domains is defined via uniform domains and the Loewner property. Using prime ends… read more here.
Keywords: prime ends; heisenberg group; group boundary; quasiconformal mappings ... See more keywords
Quasiconformal mappings with controlled Laplacian and Hölder continuity
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DOI: 10.5186/aasfm.2019.4440
Abstract: Abstract. We prove that every K-quasiconformal mapping w of the unit ball B ⊂ R, n ≥ 2 onto a C-Jordan domain Ω is Hölder continuous with constant α = 2 − n p ,… read more here.
Keywords: controlled laplacian; lder continuity; mappings controlled; quasiconformal mappings ... See more keywords