Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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LOGARITHMIC CAPACITY UNDER CONFORMAL MAPPINGS OF THE UNIT DISC

  • Chung, Bohyun (Mathematics Section, College of Science and Technology Hongik University)
  • Received : 2010.03.29
  • Accepted : 2010.06.01
  • Published : 2010.09.30
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Abstract

If P(f, r) is the set of endpoints of radii which have length greater than or equal to r > 0 under a conformal mapping f of the unit disc. Then for large r, the logarithmic capacity of P(f, r), $\frac{1}{\sqrt[2]{r}}{\leq}cap(P(f,r)){\leq}\frac{k}{\sqrt{r}}$. Where k is the positive constant.

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Acknowledgement

Supported by : Hongik University

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