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Let $f=h+\overline{g}$ 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.
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참고문헌 (14)
참고문헌 신청
S. Chen / 2015 / Stable geometric properties of pluriharmonic and biholomorphic mappings, and Landau-Bloch's theorem / Monatsh. Math. 177(1):33~51
S. Chen / 2016 / Linear connectivity, Schwarz-Pick lemma and univalency criteria for planar harmonic mapping / Acta Math. Sin. (Engl. Ser.) 32(3):297~308
M. Chuaqui / 2007 / Univalent harmonic mappings and linearly connected domains / J. Math. Anal. Appl. 332(2):1189~1194
J. Clunie / 1984 / Harmonic univalent functions / Ann. Acad. Sci. Fenn. Ser. A I Math. 9:3~25
L. de Branges / 1985 / A proof of the Bieberbach conjecture / Acta Math. 154(1-2):137~152
S. Chen / 2016 / Linear connectivity, Schwarz-Pick lemma and univalency criteria for planar harmonic mapping / Acta Math. Sin. (Engl. Ser.) 32(3):297~308
M. Chuaqui / 2007 / Univalent harmonic mappings and linearly connected domains / J. Math. Anal. Appl. 332(2):1189~1194
J. Clunie / 1984 / Harmonic univalent functions / Ann. Acad. Sci. Fenn. Ser. A I Math. 9:3~25
L. de Branges / 1985 / A proof of the Bieberbach conjecture / Acta Math. 154(1-2):137~152
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