@article{Zhong2026, 
author = {Deguang Zhong and Meilan Huang},
title = {Some properties for    (  K  ,      K    ′    )-quasiconformal harmonic mappings to half-planes},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {4},
pages = {2539-2547},
keywords = {harmonic mapping, (K, K′)-quasiconformal mapping, distortion theorem, coefficient estimate, area theorem},
url = {https://www.sciopen.com/article/10.3934/era.2026117},
doi = {10.3934/era.2026117},
abstract = {Let        U   be the open unit disk,    Ω  =  {  ω  ∈      C    :      R    e      ω  >  a  ,  −  ∞  <  a  <      a          0        <  +  ∞  } with    a  ,      a          0        ∈      R  , and    K  ≥  1 and        K    ′    ≥  0 as two given constants. In this paper, we study some properties of the class        H    (      U    ,  Ω  ) of mappings consisting of those sense-preserving Euclidean harmonic mappings from        U   onto    Ω with the real, normalized conditions of    f  (  0  )  =      a          0        ,      f          z        (  0  )  >  0 and        f                  z        ¯              (  0  ). We first show that a    (  K  ,      K    ′    )-quasiconformal mapping    f  ∈      H    (      U    ,  Ω  ) need not be Euclidean Lipschitz continuous. Subsequently, we give a sufficient and necessary condition for    f  ∈      H    (      U    ,  Ω  ) to be    (  K  ,      K    ′    )-quasiconformal. Additionally, coefficient estimates, distortion theorems, and area theorems are obtained.}
}