Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0878.31003
Błocki, Zbigniew
The complex Monge-Ampère operator in hyperconvex domains. (English)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 23, No.4, 721-747 (1996). ISSN 0391-173X

Let $\Omega$ be a hyperconvex domain in $\bbfC^n$, i.e. any boundary point of $\Omega$ admits a weak plurisubharmonic barrier. The author considers such domains and proves the following result. \par Let $\Omega$ be as above, suppose that $f\in C(\partial\Omega)$ can be continuously extended to a plurisubharmonic function on $\Omega$, and let $F$ be continuous up to $\Omega$, $F\geq 0$. Then there exists a plurisubharmonic function $u\in C(\overline{\Omega})$ such that $$\text{det}\Biggl( \frac{\partial^2\psi} {\partial z_j\partial\overline{z}_k} \Biggr)=F$$ and $u|_{\partial\Omega}=f$.
[P.Z.Agranovich (Khar'kov)]

MSC 2000:: *31C10 Pluriharmonic and plurisubharmonic functions
32W20 Complex Monge-Ampère operators

Keywords: plurisubharmonic function; hyperconvex domain

Cited in: Zbl 1104.32013 Zbl 1066.32036

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]