In the present article, we obtain an optimal support function of weighted $L^2$ integrations on superlevel sets of weights of multiplier ideal sheaves, which implies the strong openness property of multiplier ideal sheaves.
In this note, we reveal that our solution of Demaillys strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Koll{a}r and Jonsson-Mustatu{a} implies the truth of twist
In this article, we establish a sharp effectiveness result of Demaillys strong openness conjecture. We also establish a sharp effectiveness result related to a conjecture posed by Demailly and Kollar.
We describe the boundary behaviors of the squeezing functions for all bounded convex domains in $mathbb{C}^n$ and bounded domains with a $C^2$ strongly convex boundary point.