Quasiconformal extension for harmonic mappings on finitely connected domains
Comptes Rendus. Mathématique, 2021 We prove that a harmonic quasiconformal mapping defined on a finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits a quasiconformal extension to the whole plane if its Schwarzian derivative is ...
Efraimidis, Iason
doaj +1 more source
Triangular Ratio Metric Under Quasiconformal Mappings in Sector Domains [PDF]
Computational methods in Function Theory, 2020 The hyperbolic metric and different hyperbolic type metrics are studied in open sector domains of the complex plane. Several sharp inequalities are proven for them.
O. Rainio, M. Vuorinen
semanticscholar +1 more source
Quasiconformal mappings and curvatures on metric measure spaces
Pracì Mìžnarodnogo Geometričnogo Centru, 2023 In an attempt to develop higher-dimensional quasiconformal mappings on metric measure spaces with curvature conditions, i.e. from Ahlfors to Alexandrov, we show that for n≥2 a noncollapsed RCD(0,n) space with Euclidean volume growth is an n-Loewner space
Jialong Deng
doaj +1 more source
Harmonic quasiconformal mappings between $\mathcal{C}^1$ smooth Jordan domains [PDF]
Revista matemática iberoamericana, 2020 We prove the following result. If $f$ is a harmonic quasiconformal mapping between two Jordan domains $D$ and $\Omega$ having $\mathscr{C}^1$ boundaries, then the function $f$ is globally H\"older continuous for every ...
D. Kalaj
semanticscholar +1 more source
dbar-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy [PDF]
, 2001 It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal Whitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane.
Ahlfors +26 more
core +2 more sources
Isolated singularities of mappings with the inverse Poletsky inequality
Математичні Студії, 2021 The manuscript is devoted to the study of mappings with finite distortion, which have been actively studied recently. We consider mappings satisfying the inverse Poletsky inequality, which can have branch points.
E.A. Sevost'yanov
doaj +1 more source
Quasiconformal, Lipschitz, and BV mappings in metric spaces [PDF]
Advances in Calculus of Variations, 2022 Consider a mapping f : X → Y {f\colon X\to Y} between two metric measure spaces. We study generalized versions of the local Lipschitz number Lip f {\operatorname{Lip}f} , as well as of the distortion number H f {H_{f}} that is used to define ...
P. Lahti
semanticscholar +1 more source
BOHR PHENOMENON FOR THE SPECIAL FAMILY OF ANALYTIC FUNCTIONS AND HARMONIC MAPPINGS
Проблемы анализа, 2020 In this paper we obtain the sharp Bohr radius for a family of bounded analytic functions B` and for the family of sensepreserving K-quasiconformal harmonic mappings of the form f = h + ¬g , where h ∈ B`
S. A. Alkhaleefah
doaj +1 more source
ON DISTORTION OF THE MODULI OF RINGS UNDER LOCALLY QUASICONFORMAL MAPPINGS IN R^n
Проблемы анализа, 2015 Some of the earlier results of author concerning distortion of the moduli of ring domains under planar locally quasiconformal mappings are generalized on the case of locally quasiconformal mappings in Rn, n ≥ 2.
S. Yu. Graf
doaj +1 more source
On boundary extension of one class of mappings in terms of prime ends
Математичні Студії, 2020 Here we consider the classes of mappings of metric spaces that distort the modulus of families of paths similarly to Poletsky inequality. For domains, which are not locally connected at the boundaries, we obtain results on the boundary extension of the ...
E.A. Sevost'yanov +2 more
doaj +1 more source