# The star function for meromorphic functions of several complex variables

## TL;DR

This paper introduces a new star function concept for meromorphic functions of multiple complex variables, extending classical ideas and characterizing functions with harmonic star functions.

## Contribution

It defines an analogue of the Baernstein star function for several variables and characterizes functions with harmonic star functions.

## Key findings

- The star function is subharmonic on the upper half-plane.
- Characterization of meromorphic functions with harmonic star functions.

## Abstract

We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes some of the main functionals attached to f.We then characterize meromorphic functions admitting a harmonic star function.