Extremal domains for the first eigenvalue of the Laplace-Beltrami operator (Q1013019)
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scientific article; zbMATH DE number 5548999
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extremal domains for the first eigenvalue of the Laplace-Beltrami operator |
scientific article; zbMATH DE number 5548999 |
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Extremal domains for the first eigenvalue of the Laplace-Beltrami operator (English)
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29 April 2009
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The main result of this paper is a proof for the existence of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator for certain Riemannian metrics. The domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.
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extremal domain
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Laplace-Beltrami operator
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first eigenvalue
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scalar curvature
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geodesic sphere
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