Skip to main content
SpringerLink
Log in

Grunsky coefficient inequalities, Caratheodory metric and extremal quasiconformal mappings

  • Published:
Commentarii Mathematici Helvetici

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Ahlfors, L. V. Remarks on the Neumann-Poincaré integral equation. Pacif. J. Math.,2 (1952), 271–280.

    MathSciNet  Google Scholar 

  2. Grunsky, H. Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen Math. Z.,45 (1939), H. 1, 29–61.

    Article  MathSciNet  Google Scholar 

  3. Kra, I. The Carathéodory metric on Abelian Teichmüller disks. J. d’Analyse Math.,40 (1981), 129–143.

    MathSciNet  Google Scholar 

  4. Krushkal’, S. L. Invariant metrics on Teichmüller spaces and quasiconformal extendability of analytic functions. Ann. Acad. Sci. Fenn., Ser. AI. Math.,10 (1985), 249–253.

    MathSciNet  Google Scholar 

  5. Krushkal’, S. L. On the Grunsky coefficient conditions. Sibirian Math. J.,28 (1987), N1, 138–145.

    MathSciNet  Google Scholar 

  6. Krushkal’, S. L. A new approach to the variational problems of the theory of quasiconformal mappings. Doklady Akad. Nauk SSSR, 292 (1987), N6, 1297–1300.

    MathSciNet  Google Scholar 

  7. Kühnau, R. Verzerrungssatze und Koeffizientenbedingungen vom Grunskyschen Typ für quasikonforme Abbildungen. Math. Nachr.,48 (1971), 77–105.

    MathSciNet  Google Scholar 

  8. Kühnau, R. Wann sind die, Grunskyschen Koeffizientenbedingungen hinreichend für Q-quasikonforme Fortsetzbarkeit? Comment. Math. Helv.,61 (1986), 290–307.

    MathSciNet  Google Scholar 

  9. Milin, I. M. Univalent functions and ortonormal systems, Nauka: Moscow, 1975.

    Google Scholar 

  10. Reich, E. On the relation between local and global properties of boundary values for extremal quasiconformal mappings.-In: Discontinuous Groups and Riemann Surfaces. Princeton: Princeton Univ. Press, 1974, p. 391–407 (Ann. of Math. Stud., 79).

    Google Scholar 

  11. Reich, E. Quasiconformal mappings of the disk with given boundary values.-In. Advances in Complex Function Theory, Berlin-Heidelberg-New York: Springer, 1976, p. 101–137 (Lecture Notes in Math., 505).

    Chapter  Google Scholar 

  12. Schiffer, M. Fredholm eigenvalues and Grunsky matrices. Ann. Polon. Math.,39 (1981), 149–164.

    MathSciNet  Google Scholar 

  13. Schober, G. Estimates for Fredholm eigenvalues based on quasiconformal mappings.-In: Numerische, insbesondere approximationstheoretische Behandlung von Funktionalgleichungen, Berlin-Heidelberg-New York: Springer, 1973, p. 211–217.

    Chapter  Google Scholar 

  14. Springer, G. Fredholm eigenvalues and quasiconformal mapping. Acta Math.,111 (1964). 121–142.

    Article  MathSciNet  Google Scholar 

  15. Strebel, K. On the existence of extremal Teichmüller mapping. J. d’Analyse Math.,30 (1976), 464–480.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Sibirian Branch of the USSR Academy of Sciences, 630090, Novosibirsk, USSR

    S. L. Krushkal’

Authors
  1. S. L. Krushkal’
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krushkal’, S.L. Grunsky coefficient inequalities, Caratheodory metric and extremal quasiconformal mappings. Commentarii Mathematici Helvetici 64, 650–660 (1989). https://doi.org/10.1007/BF02564699

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02564699

Keywords

Search

Navigation