Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME APPLICATIONS OF EXTREMAL LENGTH TO ANALYTIC FUNCTIONS

  • CHANG BO-HYUN (Mathematics Section College of Science and Technology Hong-Ik University)
  • Published : 2006.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

We consider some applications of extremal length to the boundary behavior of analytic functions and derive theorems in connection with the conformal mappings. It shows us the usefulness of the method of extremal length. And we present some geometric applications of extremal length. The method of extremal length lead to simple proofs of theorems.

Keywords

References

  1. L. V. Ahlfors, Conformal Invariants. Topics in Geometric Function Theory, McGraw-Hill, New York, 1973
  2. L. V. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand, 1987
  3. L. V. Ahlfors and A. Beurling, Conformal invariants and function-theoretic null-sets, Acta. Math. 83 (1950), 101-129 https://doi.org/10.1007/BF02392634
  4. L. V. Ahlfors and L. Sario, Riemann Surfaces, Princeton Math. Ser. 26 (1960)
  5. E. F. Collingwood and A. J. Lohwater, The Theory of Cluster Sets, Cambridge Univ. Press, London and New York, 1966
  6. H. Grotzsch, Uber einige extremal probleme der konformer abbildung, Ber. Verh. Sachs. Akad. Wiss., Leipzig. 80 (1928), 367-376
  7. K. Haliste, Estimates of harmonic measure, Ark. Mat. 6 (1965), 1-31 https://doi.org/10.1007/BF02591325
  8. G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Univ. Press, Cambridge, 1934
  9. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, Springer- Verlag, New York, 1973
  10. J. E. Mcmillan, Arbitrary functions defined on plane sets, Michigan Math. J., 14 (1967), 445-447 https://doi.org/10.1307/mmj/1028999846
  11. W. Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, New Delhi, 1974
  12. L. Sario and K. Oikawa, Capacity Functions, Springer-Verlag, New York, 1969
  13. J. Vaisala, Lectures on n-Dimensional Quasiconformal Mappings, Springer- Verlag, New York, 1971
  14. J. Vaisala, On quasiconformal mappings in space, Ann. Acad. Sci. Fenn. Ser. AI. 298 (1961), 1-35