On compactness and completeness of conformal metrics in \(\mathbb{R}^N\) (Q1382026)
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scientific article; zbMATH DE number 1136598
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On compactness and completeness of conformal metrics in \(\mathbb{R}^N\) |
scientific article; zbMATH DE number 1136598 |
Statements
On compactness and completeness of conformal metrics in \(\mathbb{R}^N\) (English)
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22 November 1998
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The following problem is considered: given a smooth function \(K(x)\) on the \(n\)-dimensional Euclidean space with Euclidean metric \(g_0\), we seek a positive function \(u\) such that the conformally flat metric \(g=u^{4/(n-2)} g_0\) has scalar curvature \(K.\) Sufficient conditions are given under which the metric \(g\) is complete with bounded curvatures.
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completeness
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conformally flat metrics
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Kazdan-Warner identity
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