On the problem of Kähler convexity in the Bergman metric (Q1766483)
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scientific article; zbMATH DE number 2141489
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the problem of Kähler convexity in the Bergman metric |
scientific article; zbMATH DE number 2141489 |
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On the problem of Kähler convexity in the Bergman metric (English)
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7 March 2005
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Let \(M\) be a complete Kähler manifold of dimension \(n\). Assume that the Kähler metric \(ds^2\) has a global potential \(V\in C^2(M)\). We say \(V\) dominates its gradient if there exist constants \(A,B\geq 0\) such that \[ | \partial V| ^2\leq A+BV \] on \(M\). The author gives an example of a smooth bounded weakly pseudoconvex domain of finite type such that the potential does not dominate its gradient.
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Kähler convexity
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Bergman metric
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smooth bounded weakly pseudoconvex domain of finite type
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