Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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DOMAINS WITH Ck CR CONTRACTIONS

  • Kim, Sung-Yeon (Department of Mathematics Education Kangwon National University)
  • Received : 2009.08.31
  • Accepted : 2010.01.18
  • Published : 2010.03.30
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Abstract

Let $\Omega$ be a domain with smooth boundary in ${\mathbb{C}}^{n+1}$ and let $p{\in}{\partial}{\Omega}$. Suppose that $\Omega$ is Kobayashi hyperbolic and p is of Catlin multi-type ${\tau}=({\tau}_0,{\ldots},{\tau}_n)$. In this paper, we show that $\Omega$ admits a $C^{k}$ contraction at p with $k{\geq}\mid{\tau}\mid+1$ if and only if $\Omega$ is biholomorphically equivalent to a domain defined by a weighted homogeneous polynomial.

Keywords

References

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