Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME ESTIMATES OF HARMONIC MEASURE

  • Chung, Bohyun (Mathematics section, College of Science and Technology, Hongik University)
  • Received : 2012.04.12
  • Accepted : 2012.06.25
  • Published : 2012.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In [2], D. Gaier has given an estimates of harmonic measure. In this paper, we generalize for the K-quasiconformal mapping the corresponding result.

Keywords

Acknowledgement

Supported by : Hongik University

References

  1. L.V. Ahlfors, Conformal Invariants. Topics in Geometric Function Theory, McGraw-Hill, New York, 1973.
  2. D. Gaier, Estimates of conformal mappings near the boundary, Indiana Univ. Math. J. 21 (1992), 581-595.
  3. W. K. Hayman, Multivalent functions, Cambridge, 1958.
  4. R. Nevanlinna, Uber eine Minimumaufgabe in der theorie der knoformen Abbildung, Nachr. Akad. wiss. Gottingen 1933, 103-115.
  5. C. Pommerenke, Uber die Kapazitat ebener Kontinuen, Math. Ann. 139 (1959), 64-75. https://doi.org/10.1007/BF01459823
  6. J. Vaisala, On quasiconformal mappings in space, Ann. Acad. Sci. Fenn. AI 298, 1961, 1-36.
  7. S. E. Warschawski, On differentiability at the boundary in conformal mapping, Proc. Amer. Math. Soc. 12 (1961), 614-620. https://doi.org/10.1090/S0002-9939-1961-0131524-8
  8. S. E. Warschawski, On Holder continuity at the boundary in conformal maps, J. Math. Mech. 18 (1968), 423428.
  9. Bohyun Chung, A note on geometric applications of extremal length (I), J. Appl. Math. and Computing., 18 (2005), no. 1-2, 603-611.
  10. Bohyun Chung, Some applications of extremal length to analytic functions, Commn. Korean Math. Soc., 21 (2006), no. 1, 135-143. https://doi.org/10.4134/CKMS.2006.21.1.135
  11. Bohyun Chung, Some applications of extremal length to conformal imbeddings, J. Chungcheong Math. Soc., 22 (2009), no. 2, 507-528.