Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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QUASICONFORMAL EXTENSIONS OF STARLIKE HARMONIC MAPPINGS IN THE UNIT DISC

  • Received : 2012.11.08
  • Published : 2013.07.31
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Abstract

Let $f$ be a harmonic mapping on the unit disc ${\Delta}$ in $\mathbb{C}$. We give some condition for $f$ to be a quasiconformal homeomorphism on ${\Delta}$ and to have a quasiconformal extension to the whole plane $\bar{\mathbb{C}}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order ${\alpha}{\in}(0,1)$.

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References

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