# Hausdorff dimension of escaping sets of Nevanlinna functions

## TL;DR

This paper calculates the precise Hausdorff dimensions of escaping sets for a class of meromorphic functions with polynomial Schwarzian derivatives, linking these dimensions to associated second order differential equations.

## Contribution

It provides exact Hausdorff dimension values for escaping sets of specific meromorphic functions, a novel connection to complex differential equations.

## Key findings

- Exact Hausdorff dimensions of escaping sets determined.
- Established relation between meromorphic functions and differential equations.
- New insights into the geometric structure of escaping sets.

## Abstract

We determine the exact values of Hausdorff dimensions of escaping sets of meromorphic functions with polynomial Schwarzian derivatives. This will follow from the relation between these functions and the second order differential equations in the complex plane.