SOME RESULTS FOR THE EXTREMAL LENGTHS OF CURVE FAMILIES (II)

  • Chung, Bo-Hyun (Mathematics Section, College of Science and Technology, Hongik University)
  • Published : 2004.05.01

Abstract

We consider the applications of extremal length to the boundary behavior of analytic functions and derive a theorem in connection with the capacity. This theorem applies the extremal length to the analytic functions defined on the domain with a number of holes. So it shows us the usefulness of the method of extremal length.

Keywords

References

  1. Conformal Invariants. Topics in Geometric Function Theory L. V. Ahlfors
  2. Acta. Math. v.83 Conformal invariants and function-theoretic null-sets L. V. Ahlfors;A. Beurling
  3. Z. Math. Logik Grundlagen Math. v.12 Ambiguous points of arbitrary planar sets and functions F. Bagemihi
  4. The Theory of Cluster Sets E. F. Collingwood;A. J. Lohwater
  5. Ark. Mat. v.6 Estimates of harmonic measure K. Haliste
  6. Inequalities G. H. Hardy;J. E. Littlewood;G. Polya
  7. Nagoya. Math. J. v.24 On some boundary problems in the theory of conformal mappings of Jordan domains K. Matsumoto
  8. Michigan Math. J. v.9 Arbitrary functions defined on plane sets J. E. McMillan
  9. Analysis Functions R. Nervanlinna
  10. Dirichlet Problem, Extremal Length, and Prime Ends M. Ohtsuka
  11. Complex Variables Theory and Applications v.41 Extremal problems for Robin capacity M. D. O'neill;R. E. Thurman
  12. Comm. Math. Helv. v.29 Extremallangen und kapazitat A. Pfluger
  13. Bull. Amer. Math. Soc. v.80 The method of extremal length B. Rodin
  14. Capacity Functions L. Sario;K. Oikawa
  15. Journal of Mathematical Analysis and Applications v.247 Extremal problems for quasiconformal mappings Shen Yu-Liang
  16. Canadian mathematical Bulletin v.37 Geometric proofs of some classical results on boundary values for analytic functions Enrique Villamor