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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A sharp form of the Ahlfors' distortion theorem, with applications


Author: D. H. Hamilton
Journal: Trans. Amer. Math. Soc. 282 (1984), 799-806
MSC: Primary 30C50
MathSciNet review: 732121
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Abstract: The constant appearing in the asymptotic version of the Ahlfors' distortion theorem is $ 1$. Also it is shown that for mean $ 1$-valent functions $ f = z + {a_2}{z^2} \cdots \left\Vert {{a_{n + 1}}\vert - \vert{a_n}} \right\Vert \leqslant 1$ for $ n \geqslant N(f)$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0732121-3
PII: S 0002-9947(1984)0732121-3
Article copyright: © Copyright 1984 American Mathematical Society