Journal of the Mathematical Society of Japan

Lindelöf theorem for harmonic mappings

David KALAJ

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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 $f|_{\boldsymbol{T}}$.

Article information

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

Dates
First available in Project Euclid: 15 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1460727374

Digital Object Identifier
doi:10.2969/jmsj/06820653

Mathematical Reviews number (MathSciNet)
MR3488139

Zentralblatt MATH identifier
1350.31002

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

Keywords
harmonic mappings quasiconformal mappings smooth domains

Citation

KALAJ, David. Lindelöf theorem for harmonic mappings. J. Math. Soc. Japan 68 (2016), no. 2, 653--667. doi:10.2969/jmsj/06820653. https://projecteuclid.org/euclid.jmsj/1460727374


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