Results 1 to 10 of about 1,270,291 (205)
Finely quasiconformal mappings [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2022 We introduce a relaxed version of the metric definition of quasiconformality that is natural also for mappings of low regularity, including $W_{\mathrm{loc}}^{1,1}({\mathbb R}^n;{\mathbb R}^n)$ -mappings. Then we show on the plane that this relaxed definition can be used to prove Sobolev regularity, and that these ‘finely ...
P. Lahti
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1-Quasiconformal Mappings and CR Mappings on Goursat Groups [PDF]
The Scientific World Journal, 2014 We show that 1-quasiconformal mappings on Goursat groups are CR or anti-CR mappings. This can reduce the determination of 1-quasiconformal mappings to the determination of CR automorphisms of CR manifolds, which is a fundamental problem in the theory of ...
Qing Yan Wu, Zun Wei Fu
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Area distortion under certain classes of quasiconformal mappings [PDF]
Journal of Inequalities and Applications, 2017 In this paper we study the hyperbolic and Euclidean area distortion of measurable sets under some classes of K-quasiconformal mappings from the upper half-plane and the unit disk onto themselves, respectively.
Alfonso Hernández-Montes +1 more
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Duality of Moduli and Quasiconformal Mappings in Metric Spaces [PDF]
Analysis and Geometry in Metric Spaces, 2020 We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality.
Jones Rebekah, Lahti Panu
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Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale [PDF]
Journal des Mathématiques Pures et Appliquées, 2019 We give sufficient conditions for quasiconformal mappings between simply connected Lipschitz domains to have H\"older, Sobolev and Triebel-Lizorkin regularity in terms of the regularity of the boundary of the domains and the regularity of the Beltrami ...
Astala, Kari +2 more
core +4 more sources
Quasiconformal curves and quasiconformal maps in metric spaces
Analysis and Geometry in Metric SpacesIn this article, we study quasiconformal curves which are a special case of quasiregular curves. Namely embeddings Ω→Rm\Omega \to {{\mathbb{R}}}^{m} from some domain Ω⊂Rn\Omega \subset {{\mathbb{R}}}^{n} to Rm{{\mathbb{R}}}^{m}, where n≤mn\le m, belong ...
Hitruhin Lauri, Tsantaris Athanasios
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Holomorphic motions, dimension, area and quasiconformal mappings [PDF]
Journal des Mathématiques Pures et Appliquées, 2023 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
Aidan Fuhrer, T. Ransford, M. Younsi
semanticscholar +1 more source
A learning-based framework for topology-preserving segmentation using quasiconformal mappings [PDF]
Neurocomputing, 2022 We propose the Topology-Preserving Segmentation Network, a deformation-based model that can extract objects in an image while maintaining their topological properties.
Han Zhang, L. Lui
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Composition operators on Hardy-Sobolev spaces and BMO-quasiconformal mappings [PDF]
Journal of Mathematical Sciences, 2021 In this paper, we consider composition operators on Hardy-Sobolev spaces in connections with BMO-quasiconformal mappings. Using the duality of Hardy spaces and BMO-spaces, we prove that BMO-quasiconformal mappings generate bounded composition operators ...
A. Menovschikov, A. Ukhlov
semanticscholar +1 more source
RINGS AND QUASICONFORMAL MAPPINGS IN SPACE. [PDF]
Proc Natl Acad Sci U S A, 1961 Gehring FW.
europepmc +7 more sources