# Regularization of plurisubharmonic functions with a net of good points

## TL;DR

This paper introduces a novel regularization method for quasi-plurisubharmonic functions on compact Kähler manifolds, utilizing local regularizations and a delta-net to ensure higher order terms vanish at centers.

## Contribution

It presents a new technique combining local regularization with a delta-net approach to improve the regularity of quasi-plurisubharmonic functions on Kähler manifolds.

## Key findings

- Higher order terms vanish at coordinate centers
- Regularization is achieved via local coordinate balls
- Centers form a delta-net covering the manifold

## Abstract

The purpose of this article is to present a new regularization technique of quasi-plurisubharmoinc functions on a compact Kaehler manifold. The idea is to regularize the function on local coordinate balls first, and then glue each piece together. Therefore, all the higher order terms in the complex Hessian of this regularization vanish at the center of each coordinate ball, and all the centers build a delta-net of the manifold eventually.