Abstract
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 $f|_{\boldsymbol{T}}$.
Citation
David KALAJ. "Lindelöf theorem for harmonic mappings." J. Math. Soc. Japan 68 (2) 653 - 667, April, 2016. https://doi.org/10.2969/jmsj/06820653
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