Toshiyuki SUGAWA
Inner radius of univalence for a strongly starlike domain
Abstract
The inner radius of univalence of a domain D with Poincar'e density
pD is the possible largest number c such that
the condition ||Sf||D
=supw
pD(w)-2|Sf
(z)| < c
implies the univalence of f for a nonconstant meromorphic function
f on D, where Sf
is the Schwarzian drivative of f.
In this note, we will give a lower estimate of the inner radius
of univalence for strongly starlike domains of order a
with a concrete bound in terms of the order a.
submission: February 4, 2000
revision: February 8, 2000
revision: November 21, 2001
revision: November 22, 2001
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