Triangular ratio metric under quasiconformal mappings in sector domains

TL;DR

This paper investigates the behavior of the triangular ratio metric in sector domains under quasiconformal mappings, providing sharp inequalities and insights into how these metrics transform.

Contribution

It introduces new sharp inequalities for hyperbolic and related metrics in sector domains and characterizes the triangular ratio metric's behavior under quasiconformal maps.

Findings

Established sharp inequalities for hyperbolic and related metrics in sector domains

Described the transformation behavior of the triangular ratio metric under quasiconformal maps

Provided new insights into metric distortion in complex analysis

Abstract

Hyperbolic metric and different hyperbolic type metrics are studied in open sector domains of the complex plane. Several sharp inequalities are proven for them. Our main result describes the behavior of the triangular ratio metric under quasiconformal maps from one sector onto another one.