SOME APPLICATIONS OF RESISTANT LENGTH TO ANALYTIC FUNCTIONS

  • Chung, Bo-Hyun (Mathematics Section, College of Science and Technology, Hongik University)
  • 발행 : 2009.09.30

초록

We introduce the resistant length and examine its properties. We also consider the geometric applications of resistant length to the boundary behavior of analytic functions, conformal mappings and derive the theorem in connection with the fundamental sequences, purely geometric problems. The method of resistant length leads a simple proofs of theorems. So it shows us the usefulness of the method of resistant length.

키워드

참고문헌

  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. Bo-Hyun Chung, Some results for the resistant lengths of curve families (II), J. Appl. Math. and Computing., 15(No. 1-2) (2004), 495-502
  4. Bo-Hyun Chung, A note on geometric applications of extremal lengths (I), J. Appl. Math. and Computing., 18(No. 1-2) (2005), 603-611.
  5. Bo-Hyun Chung, Some applications of extremal length to analytic functions, Commun. Korean. Math. Soc., 21(No. 1) (2006), 135-143. https://doi.org/10.4134/CKMS.2006.21.1.135
  6. Bo-Hyun Chung, Extremal length and geometric inequalities, J. Chungcheong.Math. Soc., 20(No. 2) (2007), 147-156.
  7. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, Springer-Verlag, New York (1973)
  8. M. D. O'neill and R. E. Thurman, Extremal problems for Robin capacity, Complex Variables Theory and Applications, 41(2000).
  9. B. Rodin, The method of extremal length, Bull. Amer. Math. Soc., 80(1974), 587-606. https://doi.org/10.1090/S0002-9904-1974-13517-2
  10. Shen Yu-Liang, Extremal problems for quasiconformal mappings, Journal of Mathematical Analysis and Applications, 247(2000), 27-44. https://doi.org/10.1006/jmaa.2000.6806
  11. J. Vaisala, Lectures on n-Dimensional Quasiconformal Mappings, Springer-Verlag, New York, (1971)