On conformal distortion and Sullivan’s sector theorem
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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.References
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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
- MR Author ID: 357550
- Email: edson@ime.usp.br
- Received by editor(s): November 21, 1994
- Additional Notes: This work has been supported by FAPESP Grant 95/3187-4.
- Communicated by: Linda Keen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 67-74
- MSC (1991): Primary 30C55, 30D05; Secondary 58F23
- DOI: https://doi.org/10.1090/S0002-9939-98-04487-6
- MathSciNet review: 1458867