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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Teichmüller inequalities without coefficient normalization


Author: Arthur E. Obrock
Journal: Trans. Amer. Math. Soc. 159 (1971), 391-416
MSC: Primary 30A36
DOI: https://doi.org/10.1090/S0002-9947-1971-0393459-6
MathSciNet review: 0393459
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0393459-6
Keywords: Schlicht functions, quadratic differentials coefficient normalization, length-area method, Teichmüller's Theorem, Jenkins' General Coefficient Theorem
Article copyright: © Copyright 1971 American Mathematical Society