A Loewner variational method in the theory of schlicht functions

Details A Loewner variational method in the theory of schlicht functions A Loewner variational method in the theory of schlicht functions

2011-12-21

arxiv.org/abs/1112.5187v1

Mathematics

Complex Variables

12 pages

Scientific paper

A Loewner variational method is developed that allows to calculate arbitrary continuous coefficient functionals of the second, third and fourth coefficients of schlicht functions. Based on this method an improved lower bound for the Milin-constant(0.034856..) is given, as well as an improved lower bound for the maximal modulus of the seventh coefficient of odd schlicht functions(1.006763..). The extremals for the generating function kappa of the Loewner differential equation are determined precisely.

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