- Tytuł:
- On a result by Clunie and Sheil-Small
- Autorzy:
-
Partyka, Dariusz
Sakan, Ken-ichi - Powiązania:
- https://bibliotekanauki.pl/articles/747161.pdf
- Data publikacji:
- 2012
- Wydawca:
- Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
- Tematy:
-
Harmonic mappings
Lipschitz condition
bi-Lipchitz condition
co-Lipchitz condition
quasiconformal mappings - Opis:
- In 1984 J. Clunie and T. Sheil-Small proved ([2, Corollary 5.8]) that for any complex-valued and sense-preserving injective harmonic mapping \(F\) in the unit disk \(\mathbb{D}\), if \(F(\mathbb{D})\) is a convex domain, then the inequality \(|G(z_2)-G(z_1)| < |H(z_2)- H(z_1)|\) holds for all distinct points \(z_1, z_2 \in \mathbb{D}\). Here \(H\) and \(G\) are holomorphic mappings in \(\mathbb{D}\) determined by \(F = H + \overline{G}\), up to a constant function. We extend this inequality by replacing the unit disk by an arbitrary nonempty domain \(\Omega\) in \(\mathbb{C}\) and improve it provided \(F\) is additionally a quasiconformal mapping in \(\Omega\).
- Źródło:
-
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2012, 66, 2
0365-1029
2083-7402 - Pojawia się w:
- Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł