Supplement to $L^2$ theory of $\bar{\partial}$ on complete K\"ahler domains

TL;DR

This paper presents a novel technique for handling $L^2$ estimates of the $ar{ ext{d}}$ operator with singular weights on complete K"ahler domains, enhancing the theoretical framework in complex analysis.

Contribution

It introduces a new method for $L^2$ estimates of $ar{ ext{d}}$ with singular weights, expanding the existing $L^2$ theory on complete K"ahler domains.

Findings

Developed a new trick for $L^2$ estimates with singular weights

Extended $L^2$ $ar{ ext{d}}$ theory to complete K"ahler domains

Provided tools for further research in complex geometry

Abstract

We introduce a trick of dealing with $L^2$ estimates of $\bar{\partial}$ with singular weights on complete K\"ahler domains.