An asymptotically sharp coefficients estimate for harmonic K-quasiconformal mappings

Harmonic Quasiconformal Mappings of Riemannian Manifolds

Quasiconformal Extension of Harmonic Mappings in the Plane

Let f be a sense-preserving harmonic mapping in the unit disk. We give a sufficient condition in terms of the pre-Schwarzian derivative of f to ensure that it can be extended to a quasiconformal map in the complex plane. Introduction A well-known criterion due to Becker [5] states that if a locally univalent analytic function φ in the unit disk D satisfies (1) sup z∈D ∣∣∣∣φ′′(z) φ′(z) ∣∣∣∣ (1− ...

On Harmonic Quasiconformal Self-mappings of the Unit Ball

It is proved that any family of harmonic K-quasiconformal mappings {u = P [f ], u(0) = 0} of the unit ball onto itself is a uniformly Lipschitz family providing that f ∈ C. Moreover, the Lipschitz constant tends to 1 as K → 1.

A new subclass of harmonic mappings with positive coefficients

‎Complex-valued harmonic functions that are univalent and‎ ‎sense-preserving in the open unit disk $U$ can be written as form‎ ‎$f =h+bar{g}$‎, ‎where $h$ and $g$ are analytic in $U$‎. ‎In this paper‎, ‎we introduce the class $S_H^1(beta)$‎, ‎where $1<betaleq 2$‎, ‎and‎ ‎consisting of harmonic univalent function $f = h+bar{g}$‎, ‎where $h$ and $g$ are in the form‎ ‎$h(z) = z+sumlimits_{n=2}^inf...

Hyperbolically Bi-Lipschitz Continuity for 1/|ω|2-Harmonic Quasiconformal Mappings

We study the class of 1/|w|-harmonic K-quasiconformal mappings with angular ranges. After building a differential equation for the hyperbolic metric of an angular range, we obtain the sharp bounds of their hyperbolically partial derivatives, determined by the quasiconformal constant K. As an applicationwe get their hyperbolically bi-Lipschitz continuity and their sharp hyperbolically bi-Lipschi...