Browse > Article
http://dx.doi.org/10.4134/CKMS.2006.21.1.135

SOME APPLICATIONS OF EXTREMAL LENGTH TO ANALYTIC FUNCTIONS  

CHANG BO-HYUN (Mathematics Section College of Science and Technology Hong-Ik University)
Publication Information
Communications of the Korean Mathematical Society / v.21, no.1, 2006 , pp. 135-143 More about this Journal
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
extremal length; boundary behavior;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, Springer- Verlag, New York, 1973
2 J. E. Mcmillan, Arbitrary functions defined on plane sets, Michigan Math. J., 14 (1967), 445-447   DOI
3 W. Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, New Delhi, 1974
4 L. Sario and K. Oikawa, Capacity Functions, Springer-Verlag, New York, 1969
5 L. V. Ahlfors, Conformal Invariants. Topics in Geometric Function Theory, McGraw-Hill, New York, 1973
6 L. V. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand, 1987
7 L. V. Ahlfors and A. Beurling, Conformal invariants and function-theoretic null-sets, Acta. Math. 83 (1950), 101-129   DOI
8 L. V. Ahlfors and L. Sario, Riemann Surfaces, Princeton Math. Ser. 26 (1960)
9 E. F. Collingwood and A. J. Lohwater, The Theory of Cluster Sets, Cambridge Univ. Press, London and New York, 1966
10 H. Grotzsch, Uber einige extremal probleme der konformer abbildung, Ber. Verh. Sachs. Akad. Wiss., Leipzig. 80 (1928), 367-376
11 K. Haliste, Estimates of harmonic measure, Ark. Mat. 6 (1965), 1-31   DOI
12 J. Vaisala, On quasiconformal mappings in space, Ann. Acad. Sci. Fenn. Ser. AI. 298 (1961), 1-35
13 G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Univ. Press, Cambridge, 1934
14 J. Vaisala, Lectures on n-Dimensional Quasiconformal Mappings, Springer- Verlag, New York, 1971