The Bergman metric on hyperconvex domains (Q1307014)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The Bergman metric on hyperconvex domains |
scientific article; zbMATH DE number 1351165
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Bergman metric on hyperconvex domains |
scientific article; zbMATH DE number 1351165 |
Statements
The Bergman metric on hyperconvex domains (English)
0 references
20 October 1999
0 references
The question of Bergman completeness is investigated. We study the class of hyperconvex domains. A domain \(\Omega\subset \mathbb{C}^n\) is called hyperconvex if it admits a continuous bounded plurisubharmonic exhaustion function. Our main result is that on hyperconvex bounded domains the Bergman metric is complete. The reverse conclusion fails in general, as is shown by an example.
0 references
Bergman kernel
0 references
\(\overline\partial\)-equation
0 references
pluricomplex Green's function
0 references
hyperconvex domains
0 references
Bergman metric
0 references
