A support function of the weighted $L^2$ integrations on the superlevel sets of the weights

TL;DR

This paper introduces a support function for weighted L^2 integrations on superlevel sets of weights, achieving optimal asymptotic behavior and relating to Demailly's strong openness conjecture.

Contribution

It establishes a novel support function for weighted L^2 integrals on superlevel sets, providing an analogue to Demailly's strong openness conjecture with optimal asymptotic properties.

Findings

Support function with optimal asymptoticity near infinity

Analogue of Demailly's strong openness conjecture

Advances understanding of weighted L^2 integrations

Abstract

In this article, we establish a support function of the weighted $L^2$ integrations on the superlevel sets of the weights with optimal asymptoticity near the positive infinity, which is an analogue of the truth of Demailly's strong openness conjecture.