Teichmüller inequalities without coefficient normalization

Obrock, Arthur E.

doi:10.1090/S0002-9947-1971-0393459-6

Teichmüller inequalities without coefficient normalization
HTML articles powered by AMS MathViewer

by Arthur E. Obrock PDF

Trans. Amer. Math. Soc. 159 (1971), 391-416 Request permission

Abstract:

Teichmüller’s relation between the coefficients of extremal schlicht functions and quadratic differentials is extended. The coefficient normalization hypothesis in his theorem is dropped with the result that the new coefficient relations become more complex. This completes the partial result in this direction which is contained in Jenkins’ General Coefficient Theorem. A modification of the version of the length-area method used by Teichmüller and Jenkins is introduced in our proof.

References

James A. Jenkins, Univalent functions and conformal mapping, Reihe: Moderne Funktionentheorie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0096806
James A. Jenkins, An addendum to the general coefficient theorem, Trans. Amer. Math. Soc. 107 (1963), 125–128. MR 147639, DOI 10.1090/S0002-9947-1963-0147639-0
James A. Jenkins, On the global structure of the trajectories of a positive quadratic differential, Illinois J. Math. 4 (1960), 405–412. MR 124482
Arthur Obrock, An inequality for certain schlicht functions, Proc. Amer. Math. Soc. 17 (1966), 1250–1253. MR 206256, DOI 10.1090/S0002-9939-1966-0206256-2
A. C. Schaeffer and D. C. Spencer, Coefficient Regions for Schlicht Functions, American Mathematical Society Colloquium Publications, Vol. 35, American Mathematical Society, New York, N. Y., 1950. With a Chapter on the Region of the Derivative of a Schlicht Function by Arthur Grad. MR 0037908

Ungleichungen zwischen den Koeffizienten schlichter Funktionen

1938