\(L^{2}\) harmonic forms and finiteness of ends (Q2865807)
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scientific article; zbMATH DE number 6235407
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^{2}\) harmonic forms and finiteness of ends |
scientific article; zbMATH DE number 6235407 |
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3 December 2013
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weighted Poincaré inequality
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\(L^2\)-harmonic forms
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0.9047729
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0.8951714
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0.89439744
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0.8936628
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0.89154696
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\(L^{2}\) harmonic forms and finiteness of ends (English)
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The author derives several vanishing theorems on complete non-compact Riemannian manifolds \(M\) satisfying a weighted Poincaré inequality with a nonnegative weight function. The main result asserts that \(H'(L^2(M))= \{0\}\) provided that \(\text{Ric}_M(x)\geq-{n\over n-1} \rho(x)+ \sigma(x)\) for continuous \(\sigma\geq 0\) and \(\rho(x)= O(r^{2-\alpha})\) with \(0<\alpha< 2\).
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