Support points and double poles

Author:
Say Song Goh

Journal:
Proc. Amer. Math. Soc. **122** (1994), 463-468

MSC:
Primary 30C50; Secondary 30C70

MathSciNet review:
1197537

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Abstract: This paper gives some sufficient conditions for support points of the class *S* of univalent functions to be rotations of the Koebe function . If *f* is a support point associated with a continuous linear functional *L* and if the function does not have a double pole, then under some mild additional assumptions, a rational support point *f* must be a rotation of the Koebe function. The situation is more complicated when has a double pole. However, we are able to prove the two-functional conjecture for derivative functionals, where has a double pole.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1197537-4

Keywords:
Univalent functions,
variational methods,
algebraic functions,
the two-functional conjecture,
derivative functionals

Article copyright:
© Copyright 1994
American Mathematical Society