相关论文: Quasiconformal harmonic mappings between $\,\maths…
We mainly investigate some properties of quasiconformal mappings between smooth 2-dimensional surfaces with boundary in the Euclidean space, satisfying certain partial differential equations (inequalities) concerning Laplacian, and in…
A quantitative version of an inequality obtained in \cite[Theorem~2.1]{mathz} is given. More precisely, for normalized $K$ quasiconformal harmonic mappings of the unit disk onto a Jordan domain $\Omega\in C^{1,\mu} $ ($0<\mu\le 1$) we give…
We establish that every $K$-quasiconformal mapping of $w$ of the unit disk $\ID$ onto a $C^2$-Jordan domain $\Omega$ is Lipschitz provided that $\Delta w\in L^p(\ID)$ for some $p>2$. We also prove that if in this situation $K\to 1$ with…
We prove that every sense-preserving harmonic $K$--quasiconformal homeomorphism $f\colon D\to\Omega$ between Lyapunov domains (equivalently, bounded $C^{1,\alpha}$ domains) in $\mathbb{R}^n$, $\alpha\in(0,1]$, is globally Lipschitz on…
We prove the following theorem: every quasiconformal harmonic mapping between two plane domains with $C^{1,\alpha}$ ($\alpha<1$), respectively $C^{1,1}$ compact boundary is bi-Lipschitz. The distance function with respect to the boundary of…
In \cite{kamz} the author proved that every quasiconformal harmonic mapping between two Jordan domains with $C^{1,\alpha}$, $0<\alpha\le 1$, boundary is bi-Lipschitz, providing that the domain is convex. In this paper we avoid the…
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 $\alpha<1$ but it is…
Let $h$ be a quasiconformal (qc) mapping of the unit disk $\mathbb{U}$ onto a Lyapunov domain. We show that $h$ maps subdomains of Lyapunov type of $\mathbb{U}$, which touch the boundary of $\mathbb{U}$, onto domains of similar type. In…
We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be…
In this article, we first discuss the Lipschitz characteristic and the linear measure distortion of $K$-quasiconformal harmonic mappings. Then we give some characterizations of the radial John disks with the help of Pre-Schwarzian of…
We prove the following. If $f$ is a harmonic quasiconformal mapping between the unit ball in $\mathbb{R}^n$ and a spatial domain with $C^{1,\alpha}$ boundary, then $f$ is Lipschitz continuous in $B$. This generalizes some known results for…
It is proved the following theorem, if $w$ is a quasiconformal harmonic mappings between two Riemann surfaces with smooth boundary and aproximate analytic metric, then $w$ is a quasi-isometry with respect to Euclidean metric.
Let $D$ and $\Omega$ be Jordan domains with Dini's smooth boundaries and and let $f:D\mapsto \Omega$ be a harmonic homeomorphism. The object of the paper is to prove the following result: If $f$ is quasiconformal, then $f$ is Lipschitz.…
We first investigate the Lipschitz continuity of $(K, K')$-quasiregular $C^2$ mappings between two Jordan domains with smooth boundaries, satisfying certain partial differential inequalities concerning Laplacian. Then two applications of…
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…
We prove that every quasiconformal mapping from the harmonic $\beta$-Bloch space between the unit ball and a spatial domain with $C^1$ boundary is globally $\alpha$-H\"older continuous for $\alpha<1-\beta$, with the H\"older coefficient…
The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected…
This article studies the smoothness of conformal mappings between two Riemannian manifolds whose metric tensors have limited regularity. We show that any bi-Lipschitz conformal mapping or $1$-quasiregular mapping between two manifolds with…
This note examines sufficient conditions for the quasiconformal extendibility of harmonic mappings defined in the unit disk. It is demonstrated that a harmonic strongly starlike mapping admits a quasiconformal extension to the entire plane,…
We prove that a self-homeomorphism of the Grushin plane is quasisymmetric if and only if it is metrically quasiconformal and if and only if it is geometrically quasiconformal. As the main step in our argument, we show that a quasisymmetric…