Estimation of weighted $L^2$ norm related to Demailly's Strong Openness Conjecture

TL;DR

This paper provides an estimation of the weighted $L^2$ norm near singularities of plurisubharmonic weights, advancing understanding related to Demailly's strong openness conjecture and demonstrating norm convergence.

Contribution

It introduces a new estimation technique for weighted $L^2$ norms that supports the strong openness conjecture in complex analysis.

Findings

Estimation of weighted $L^2$ norms near singularities

Proof of convergence of the weighted $L^2$ norm

Implications for Demailly's strong openness conjecture

Abstract

In the present article, we obtain an estimation of the weighted $L^2$ norm near the singularities of plurisubharmonic weight related to Demailly's strong openness conjecture, which implies the convergence of the weighted $L^2$ norm.