# Pluricomplex Green functions on manifolds

## TL;DR

This paper establishes foundational properties of pluricomplex Green functions on complex manifolds, aiming to identify conditions that make these manifolds analogous to well-understood domains in Stein manifolds.

## Contribution

It proves basic properties of pluricomplex Green functions on manifolds and characterizes manifolds similar to hyperconvex domains in Stein manifolds.

## Key findings

- Properties of pluricomplex Green functions are established.
- Conditions for manifolds to be analogous to hyperconvex domains are identified.
- Foundational results for pluricomplex analysis on manifolds are provided.

## Abstract

In this paper we prove the basic facts for pluricomplex Green functions on manifolds. The main goal is to establish properties of complex manifolds that make them analogous to relatively compact or hyperconvex domains in Stein manifolds. The final version to appear in JGA.