Teichmuller space theory and classical problems of geometric function theory

TL;DR

This paper applies Teichmuller space theory, especially the Bers isomorphism theorem, to address classical coefficient problems in geometric function theory, extending previous results to broader classes of functions.

Contribution

It introduces new applications of Teichmuller space methods to classical problems, expanding the scope of previous approaches in geometric function theory.

Findings

Extended coefficient bounds for broader classes of functions

Demonstrated the effectiveness of Teichmuller space techniques in classical problems

Provided new insights into the structure of holomorphic functions

Abstract

Recently the author presented a new approach to solving the coefficient problems for holomorphic functions based on the deep features of Teichmuller spaces. It involves the Bers isomorphism theorem for Teichmuller spaces of punctured Riemann surfaces. The aim of the present paper is to provide new applications of this approach and extend the indicated results to more general classes of functions