# STRONG OPENNESS CONJECTURE FOR PLURISUBHARMONIC FUNCTIONS

@article{Guan2013STRONGOC, title={STRONG OPENNESS CONJECTURE FOR PLURISUBHARMONIC FUNCTIONS}, author={Qi’an Guan and Xiangyu Zhou}, journal={arXiv: Complex Variables}, year={2013} }

In this article, we give a proof of the strong openness conjecture for plurisubharmonic functions posed by Demailly.

## 41 Citations

Modules of Square Integrable Holomorphic Germs

- Mathematics
- 2017

This paper was inspired by Guan and Zhou’s recent proof of the socalled strong openness conjecture for plurisubharmonic functions. We give a proof shorter than theirs and extend the result to…

A remark on equisingular approximations of quasi-plurisubharmonic functions

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In this note, we will present global equisingular approximations of quasi-plurisubharmonic functions with stable analytic pluripolar sets on compact complex manifolds.

Strong openness conjecture and related problems for plurisubharmonic functions

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In this article, we solve the strong openness conjecture on the multiplier ideal sheaves for the plurisubharmonic functions posed by Demailly. We prove two conjectures about the growth of the volumes…

A Degenerate Donnelly–Fefferman Theorem and its Applications

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We prove a degenerate Donnelly–Fefferman theorem. Applications to local non-integrability of plurisubharmonic functions and \(L^2\) boundary decay estimates of the Bergman kernel are given.

Strong openness of multiplier ideal sheaves and optimal L2 extension

- Mathematics
- 2017

In this paper, we reveal that our solution of Demailly’s strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Kollár and Jonsson-Mustată…

Ohsawa-Takegoshi Extension Theorem for Compact Kähler Manifolds and Applications

- Mathematics
- 2017

Our main goal in this article is to prove an extension theorem for sections of the canonical bundle of a weakly pseudoconvex Kahler manifold with values in a line bundle endowed with a possibly…

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

- Mathematics
- 2016

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…

CLASSIFICATION OF MULTIPLIER IDEAL SHEAF WITH LELONG NUMBER ONE WEIGHT

- Mathematics
- 2014

In this article, we characterize the germ of the multiplier ideal sheaf whose associated plurisubharmonic function has Lelong number one at the point. We also present a new proof of a Skoda's result.

Equivalence of plurisubharmonic singularities and Siu-type metrics

- Mathematics
- 2014

We show by an example that the (equivalence class of) singularity of a plurisubharmonic function cannot be determined by the data of its Lelong numbers, in a nontrivial sense. Such an example is…

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