Moduli of doubly connected domains and conformally invariant metrics
- 25 Downloads
It is proved that some conformal invariants associated with Teichmuller's problem on the maximum conformal modulus in a family of doubly connected domains separating two points define a metric on the perforated z-sphere. A problem posed by M. Vuorinen is solved.
KeywordsConformal Invariant Invariant Metrics Conformal Modulus
Unable to display preview. Download preview PDF.
- 1.M. Vuorinen, Conformal Geometry and Quasi-Regular Mappings, Springer-Verlag, Berlin (1988).Google Scholar
- 2.G. V. Kuz'mina, “The moduli of families of curves and quadratic differentials,” Tr. Mat. Inst. Akad. Nauk SSSR,139, (1980).Google Scholar
- 3.A. Yu. Solynin, “The relationship between modulus problems for families of several classes of curves and parameters,” Zap. Nauchn. Semin. LOMI,144, 136–145 (1986).Google Scholar
- 4.E. G. Emel'yanov, “Properties of the moduli of families of curves,” Zap. Nauchn. Semin. LOMI,144, 72–82 (1985).Google Scholar
- 5.V. N. Dubinin, “Transformation of capacitors in space,” Dokl. Akad. Nauk SSSR,296, No. 1, 18–20 (1987).Google Scholar
- 6.V. Wolontis, “Properties of conformal invariants,” Amer. J. Math.,74, No. 3, 587–606 (1952).Google Scholar