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On the Cegrell Classes Associated to a Positive Closed Current

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Chinese Annals of Mathematics,Series B 2019年第4期40卷 567-584页

作者： Mohamed ZAWAY Department of Mathematics Faculty of Sciences Ad DwadimiShaqra University Department of Mathematics Faculty of Science of Gabes University of Gabes

The aim of this paper is to study the operatoron■ on some classes of plurisubharmonic (psh) functions, which are not necessary bounded, where T is a positive closed current of bidimension (q, q) on an open set ? of C^n. The author introduces two classes F_p^T (?) and■ and shows first that they belong to the domain of definition of the operator■. Then the author proves that all functions that belong to these classes are C_T-quasi-continuous and that the comparison principle is valid for them.

关键词： Positive closed current plurisubharmonic function Capacity Monge-Ampère Operator

On interpolation for Hormander’s algebras

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Science China Mathematics 2010年第3期53卷 763-770页

作者： LI Bao Qin Department of Mathematics, Florida International University, Miami, FL 33199, USA Department of Mathematics Florida International University Miami USA

We discuss some recent results on interpolation problems for weighted Hrmander’s algebras of holomorphic functions in several complex variables, and also give a sharp estimate on counting functions of interpolating... 详细信息

关键词： weight pseudoconvex set Hrmander’s algebra interpolating variety plurisubharmonic function holomorphic function entire function

ON THE EXTENDED MATRIX DISC CONJECTURE

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Science China Mathematics 1991年第12期34卷 1422-1426页

作者：周向宇 Institute of Mathematics Academia Sinica Beijing 100080 PRC

Let Pn={Z=（Z1,…,Zn）|ZiZini are 2×2 complex matrices},Hn={W=（W1,…, Wn）|Wi=ZiB,（Z1,…,Zn）∈Pn,B∈SL（2,C）}, Dn={W=（W1,…,Wn）| Wi=AZiB,（Z1,…,Zn）∈Pn,A, B∈SL（2, C）}. Are Hn,Dn domains of holomorphy? In the present paper, we prove that H2, D2 are domains of holomorphy by using the follow-ing proposition: H2={W∈C2[2×2]|W1W2*∈P1, |detW1|2|<1}.

关键词： domain of holomorphy extended matrix disc conjecture plurisubharmonic function.

Invariant holomorphic extension in several complex variables Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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Science China Mathematics 2006年第11期49卷 1593-1598页

作者： ZHOU Xiangyu Institute of Mathematics AMSS Beijing Chinese Academy of Sciences

Two fundamental problems on the invariant holomorphic extensions have been posed, which are naturally arose from our solution of the extended future tube conjecture and closely and deeply related to the general theory of Stein manifolds due to Cartan-Serre. In this paper, the relationship is presented between the two problems, the motivation of considering the problems, and the methods to approach the problems. We have also posed some questions and conjectures related to this two problems.

关键词： Stein manifold, group action, plurisubharmonic function, minimum principle, categorical quotient.