Bounds of eigenfunctions of the Laplacian on compact Riemannian manifolds (Q5953436)
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scientific article; zbMATH DE number 1694252
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bounds of eigenfunctions of the Laplacian on compact Riemannian manifolds |
scientific article; zbMATH DE number 1694252 |
Statements
Bounds of eigenfunctions of the Laplacian on compact Riemannian manifolds (English)
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24 August 2002
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Laplacian
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sectional curvature
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injectivity radius
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Let \( \varphi \) be an eigenfunction of the Laplacian with eigenvalue \( \lambda \not= 0 \). NEWLINENEWLINENEWLINEThe author proves that NEWLINE\[NEWLINE \|\varphi \|_{\infty} \leq c _1 \cdot \lambda ^{\frac{n-1}{4}} \|\varphi \|_2 NEWLINE\]NEWLINE where \( n \) is the dimension of \( M \) and \( c _1 \) depends only upon a bound for the absolute value of the sectional curvature of \( M \) and a lower bound for the injectivity radius of \( M \).
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