Comparison geometry with integral curvature bounds (Q1380464)
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scientific article; zbMATH DE number 1123719
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Comparison geometry with integral curvature bounds |
scientific article; zbMATH DE number 1123719 |
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Comparison geometry with integral curvature bounds (English)
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4 March 1998
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The authors generalize a formula of Heintze and Karcher for the volume of normal tubes around geodesics to a situation where one has integral bounds for the sectional curvature. This formula leads to a generalization of Cheeger's lemma for the length of the shortest closed geodesic and to a generalization of the Grove-Petersen finiteness result to a situation where one has integral curvature bounds.
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integral bounds for sectional curvature
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length of shortest closed geodesic
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volume of normal tubes around geodesics
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finiteness
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