Extrinsic upper bounds for \(\lambda _ 1\) (Q1093182)
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scientific article; zbMATH DE number 4022087
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extrinsic upper bounds for \(\lambda _ 1\) |
scientific article; zbMATH DE number 4022087 |
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Extrinsic upper bounds for \(\lambda _ 1\) (English)
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1988
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We derive several sharp upper bounds for \(\lambda _ 1\), the first eigenvalue of the Laplacian of a compact immersed submanifold in terms of the second fundamental form. In connection with these upper bounds we define new Riemannian invariants \(c_ n(\bar M)\), \(1\leq n\leq \dim \bar M\).
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first eigenvalue of the Laplacian
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immersed submanifold
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second fundamental form upper bounds
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Riemannian invariants
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0.89301014
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0.8717922
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0.8702317
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0.86278445
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0.8611387
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