# Singularities of local Ahlfors currents

## TL;DR

This paper proves that a complex curve charged by a local Ahlfors current must be either a disc or an annulus, providing a classification of such curves based on their geometric structure.

## Contribution

The work establishes a clear classification of complex curves charged by local Ahlfors currents, showing they are limited to discs or annuli, which advances understanding of Ahlfors currents in complex geometry.

## Key findings

- A complex curve charged by a local Ahlfors current is either a disc or an annulus.
- The result constrains the geometric possibilities for such curves.
- Provides a classification theorem in the context of complex currents.

## Abstract

We prove that a complex curve charged by a local Ahlfors current is either a disc or an annulus.