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Colloquium Mathematicum
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Colloquium Mathematicum
Article . 2003 . Peer-reviewed
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https://dx.doi.org/10.4064/cm9...
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Global pinching theorems for minimal submanifolds in spheres

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2003 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Colloquium Mathematicum, volume 96, pages 225-234 (issn: 0010-1354, eissn: 1730-6302, Copyright policy )
Authors: Cai, Kairen;

doi: 10.4064/cm96-2-7

Global pinching theorems for minimal submanifolds in spheres

Abstract

The author proves some rigidity theorems. The framework is a compact submanifold with parallel mean curvature vector embedded in the unit sphere. Sobolev inequalities of P. Li are used as a tool to get estimates for the norms of certain tensors related to the second fundamental form of the compact submanifold conditions for the latter to be a minimal submanifold in the sphere are provided.

Keywords

minimal submanifold, Global submanifolds, Sobolev inequality, mean curvature, Global Riemannian geometry, including pinching

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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