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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On conformal distortion
and Sullivan's sector theorem


Author: Edson de Faria
Journal: Proc. Amer. Math. Soc. 126 (1998), 67-74
MSC (1991): Primary 30C55, 30D05; Secondary 58F23
MathSciNet review: 1458867
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Abstract: Using general bounds on the conformal distortion of univalent maps, we prove a strong version of Sullivan's sector theorem, which gives certain sufficient conditions for an arbitrarily long composition of univalent Herglotz functions to map the upper half-plane into a proper sub-sector.


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Additional Information

Edson de Faria
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Butantã CEP05508-900 São Paulo SP, Brasil
Email: edson@ime.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04487-6
PII: S 0002-9939(98)04487-6
Keywords: Non-linearity, conformal distortion, univalent mappings
Received by editor(s): November 21, 1994
Additional Notes: This work has been supported by FAPESP Grant 95/3187-4.
Communicated by: Linda Keen
Article copyright: © Copyright 1998 American Mathematical Society