Some coefficient problems and applications

Yuk Jaum Leung and Glenn E. Schober

Vol. 145 (1990), No. 1, 71–95

DOI: 10.2140/pjm.1990.145.71

Abstract

We combine Bombieri’s method of second variation and Schiffer’s variation by truncation to consider coefficient conjectures on log f′, log f∕z, and log zf′∕f where f is a normalized univalent analytic function in |z| > 1. Related results apply to the geometric properties of extremal functions for more general linear problems. Another by-product is a simplified approach to the geometric structure of solutions to the N-th diameter problem.

Mathematical Subject Classification 2000

Primary: 30C50

Secondary: 30C45

Milestones

Received: 28 October 1988

Published: 1 September 1990