Maximum principles and its applications to submanifolds (Q2752888)
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scientific article; zbMATH DE number 1665622
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximum principles and its applications to submanifolds |
scientific article; zbMATH DE number 1665622 |
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19 August 2003
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spherical cylinders
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constant mean curvature
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nonnegative sectional curvature
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0.94790465
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0.9447826
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0.93851274
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0.9319116
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0.9170067
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0.9161762
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Maximum principles and its applications to submanifolds (English)
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The author discusses known theorems characterizing spherical cylinders \(S^k\times E^{n-k}\subset E^{n+p}\) among complete submanifolds by curvature conditions. The results are based on the generalized maximum principle of \textit{H. Omori} [Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19, 201-214 (1967; Zbl 0154.21501)], and generalizations. The point is a wrong generalization by \textit{K. Motomiya} [Nagoya Math. J. 81, 57-72 (1981; Zbl 0468.53032)]. The author gives new proofs of several theorems avoiding Motomiya's result.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00049].
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