✦ LIBER ✦
On boundary correspondences under quasiconformal harmonic mappings between smooth Jordan domains
✍ Scribed by David Kalaj
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 139 KB
- Volume
- 285
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
A quantitative version of an inequality obtained in [8, Theorem 2.1] is given. More precisely, for normalized K quasiconformal (q.c.) harmonic mappings of the unit disk onto a Jordan domain Ω ∈ C^1, μ^ (0 < μ ≤ 1), we give an explicit Lipschitz constant depending on the structure of Ω and on K. In addition, we give a characterization of q.c. harmonic mappings of the unit disk onto an arbitrary Jordan domain with C^2, α^ boundary in terms of the boundary function using the Hilbert transform. Moreover, a sharp explicit quasiconformal constant is given in terms of the boundary function.