Some examples in \(L^ p\) spectral geometry (Q686094)
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scientific article; zbMATH DE number 427752
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some examples in \(L^ p\) spectral geometry |
scientific article; zbMATH DE number 427752 |
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Some examples in \(L^ p\) spectral geometry (English)
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18 October 1993
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The authors construct a family of tori, \(T^ p_{x_ 0}\), which have the following properties for any \(p>1\): (i) The volumes and the \(L_ p\)-norms of Ricci tensor are bounded above and below uniformly in \(x_ 0\). (ii) The Cheeger constants \(h(T^ p_{x_ 0})\to 0\) as \(x_ 0 \to \infty\). (iii) \(\lambda_ 1(T^ p_{x_ 0})\) is bounded from below uniformly in \(x_ 0\).
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spectral geometry
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Laplacian
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tori
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