• 제목/요약/키워드: Quasiconformal mapping

검색결과 6건 처리시간 0.021초

QUASICONFORMAL EXTENSIONS OF STARLIKE HARMONIC MAPPINGS IN THE UNIT DISC

  • Hamada, Hidetaka;Honda, Tatsuhiro;Shon, Kwang Ho
    • 대한수학회보
    • /
    • 제50권4호
    • /
    • pp.1377-1387
    • /
    • 2013
  • Let $f$ be a harmonic mapping on the unit disc ${\Delta}$ in $\mathbb{C}$. We give some condition for $f$ to be a quasiconformal homeomorphism on ${\Delta}$ and to have a quasiconformal extension to the whole plane $\bar{\mathbb{C}}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order ${\alpha}{\in}(0,1)$.

ESTIMATES OF QUASICONFORMAL MAPPINGS NEAR THE BOUNDARY

  • Chung, Bo-Hyun;Kim, Sang Wook
    • 충청수학회지
    • /
    • 제13권1호
    • /
    • pp.39-44
    • /
    • 2000
  • In [2], D. Gaier has given an estimate of conformal mappings near the boundary. In this paper, we generalize for the K-quasiconformal mapping the corresponding result.

  • PDF

BI-LIPSCHITZ PROPERTY AND DISTORTION THEOREMS FOR PLANAR HARMONIC MAPPINGS WITH M-LINEARLY CONNECTED HOLOMORPHIC PART

  • Huang, Jie;Zhu, Jian-Feng
    • 대한수학회보
    • /
    • 제55권5호
    • /
    • pp.1419-1431
    • /
    • 2018
  • Let $f=h+{\bar{g}}$ be a harmonic mapping of the unit disk ${\mathbb{D}}$ with the holomorphic part h satisfying that h is injective and $h({\mathbb{D}})$ is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

Teichmuller extremal mappings on the unit disk

  • Keum, J.H.;Lee, M.K.
    • 대한수학회논문집
    • /
    • 제11권2호
    • /
    • pp.359-366
    • /
    • 1996
  • In this paper, we provide two Teichm$\ddot{u}$ller extremal mappings of the unit disk, having different boundary values but the same dilatation.

  • PDF

HARDY-LITTLEWOOD PROPERTY AND α-QUASIHYPERBOLIC METRIC

  • Kim, Ki Won;Ryu, Jeong Seog
    • 대한수학회논문집
    • /
    • 제35권1호
    • /
    • pp.243-250
    • /
    • 2020
  • Hardy and Littlewood found a relation between the smoothness of the radial limit of an analytic function on the unit disk D ⊂ ℂ and the growth of its derivative. It is reasonable to expect an analytic function to be smooth on the boundary if its derivative grows slowly, and conversely. Gehring and Martio showed this principle for uniform domains in ℝ2. Astala and Gehring proved quasiconformal analogue of this principle for uniform domains in ℝn. We consider α-quasihyperbolic metric, kαD and we extend it to proper domains in ℝn.