Quasiconformal mappings in the complex plane

Journal of the Mathematical Society of Japan, 2021
We prove that the energy density of uniformly continuous, quasiconformal mappings, omitting two points in CP, is equal to zero. We also prove the sharpness of this result, constructing a family of uniformly continuous, quasiconformal mappings, whose ...
H. Gaussier, M. Tsukamoto
semanticscholar +1 more source

Quasiconformal extension of integral transforms of analytic and harmonic mappings

Complex Variables and Elliptic Equations, 2022
In this article, we prove a criterion for quasiconformal extension of the integral transforms of analytic functions defined in the unit disk of the complex plane.
B. Bhowmik, Goutam Satpati
semanticscholar +1 more source

Criteria for univalency and quasiconformal extension for harmonic mappings

Kodai Mathematical Journal, 2021
In this paper, we study the univalency and quasiconformal extension of sense-preserving harmonic mappings $f$ in the unit disk. For $f$, we introduce a quantity similar to Ahlfors's criteria and obtain a criterion of univalency and quasiconformal ...
Zhenyong Hu, Jinhua Fan
semanticscholar +1 more source

mathematics