# Alexandrov-Bakelman-Pucci type estimate for plurisubharmonic functions

## TL;DR

This paper establishes an optimal Alexandrov-Bakelman-Pucci type estimate for plurisubharmonic functions without requiring continuity, extending previous results and addressing open problems in the field.

## Contribution

It generalizes existing estimates to non-continuous plurisubharmonic functions and resolves a previously posed open problem.

## Key findings

- Proved an optimal ABP type estimate for non-continuous plurisubharmonic functions.
- Generalized a key estimate from prior work.
- Addressed and solved an open problem from earlier research.

## Abstract

We prove an optimal Alexandrov-Bakelman-Pucci type estimate for plurisubharmonic functions without assuming their continuity. This generalizes a result of Y. Wang. As a corollary we generalize an estimate from \cite{DD18}. We also address a problem posed in \cite{Wan12}.