Journal of the Mathematical Society of Japan

Lindelöf theorem for harmonic mappings


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We extend the classical Lindelöf theorem for harmonic mappings. Assume that $f$ is an univalent harmonic mapping of the unit disk $\boldsymbol{U}$ onto a Jordan domain with $C^1$ boundary. Then the function $\mathrm{arg}(\partial_\varphi(f(z))/z)$, where $z=re^{i\varphi}$, has continuous extension to the boundary of the unit disk, under certain condition on $f|_{\boldsymbol{T}}$.

Article information

J. Math. Soc. Japan, Volume 68, Number 2 (2016), 653-667.

First available in Project Euclid: 15 April 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 31A05: Harmonic, subharmonic, superharmonic functions
Secondary: 31B25: Boundary behavior

harmonic mappings quasiconformal mappings smooth domains


KALAJ, David. Lindelöf theorem for harmonic mappings. J. Math. Soc. Japan 68 (2016), no. 2, 653--667. doi:10.2969/jmsj/06820653.

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