Comparison of volumes of Riemannian manifolds (Q1876929)
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scientific article; zbMATH DE number 2094046
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Comparison of volumes of Riemannian manifolds |
scientific article; zbMATH DE number 2094046 |
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Comparison of volumes of Riemannian manifolds (English)
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20 August 2004
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In this note, the authors deduce comparisons for the volumes of a manifold~\(M\) with different metrics from the comparisons of the lengths of their shortest periodic geodesics within free homotopy classes of curves on \(M\). Their basic tool is a rigidity result by \textit{G. Besson, G. Courtois} and \textit{S. Gallot} [Geom. Funct. Anal. 5, 731--799 (1995; Zbl 0851.53032)].
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volume comparison
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length spectrum
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intersection of metrics
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