Teichmuller balls and biunivalent holomorphic functions

TL;DR

This paper explores the relationship between biunivalent holomorphic functions and Teichmuller balls, offering new conditions for biunivalence and deriving sharp distortion theorems for functions with quasiconformal extensions.

Contribution

It establishes a novel connection between biunivalent functions and Teichmuller geometry, providing new criteria and distortion theorems in geometric function theory.

Findings

New sufficient conditions for biunivalence of holomorphic functions

Deep connection between biunivalence and Teichmuller balls

Sharp distortion theorems for functions with quasiconformal extension

Abstract

Biunivalent holomorphic functions form an interesting class in geometric function theory and are connected with special functions and solutions of complex differential equations. The paper reveals a deep connection between biunivalence and geometry of Teichmuller balls and provides some sufficient conditions for biunivalence of holomorphic functions on the disk. Among the consequences, one obtains new sharp distortion theorems for univalent functions with quasiconformal extension.