Abstract
Let f = h + g be a harmonic mapping of the unit disk D with the holomorphic part h satisfying that h is injective and h(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.
Original language | English |
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Pages (from-to) | 1419-1431 |
Number of pages | 13 |
Journal | Bulletin of the Korean Mathematical Society |
Volume | 55 |
Issue number | 5 |
DOIs | |
State | Published - 2018 |
Externally published | Yes |
Keywords
- Bi-lipschitz mapping
- Harmonic mapping
- M-linearly connected domain
- Quasiconformal mapping