# Constructing Strebel differentials via Belyi maps on the Riemann sphere

## TL;DR

This paper uses Belyi maps and dessins d'enfants to explicitly construct Strebel differentials with four double poles on the Riemann sphere, leading to new explicit cone spherical metrics.

## Contribution

It introduces a novel method for constructing Strebel differentials via Belyi maps, providing explicit examples and applications to cone spherical metrics.

## Key findings

- Explicit examples of Strebel differentials with four double poles
- Construction of explicit cone spherical metrics
- Demonstration of the method's effectiveness

## Abstract

In this manuscript, by using Belyi maps and dessin d'enfants, we construct some concrete examples of Strebel differentials with four double poles on the Riemann sphere. As an application, we could give some explicit cone spherical metrics on the Riemann sphere.