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Preprint . 2006
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Geometric and Functional Analysis
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https://dx.doi.org/10.48550/ar...
Article . 2006
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Geometric and Functional Analysis
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Weighted Sobolev Inequalities and Ricci Flat Manifolds

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 26 Jan 2009Embargo end date: 01 Jan 2006 France Publisher:Springer Science and Business Media LLCJournal:Geometric and Functional Analysis, volume 18, pages 1,696-1,749 (issn: 1016-443X, eissn: 1420-8970, Copyright policy )
Authors: Minerbe, Vincent;

doi: 10.1007/s00039-009-0701-3 , 10.48550/arxiv.math/0602136

arXiv: http://arxiv.org/abs/math/0602136

Weighted Sobolev Inequalities and Ricci Flat Manifolds

Abstract

We prove a weighted Sobolev inequality and a Hardy inequality on manifolds with nonnegative Ricci curvature satisfying an inverse doubling volume condition. It enables us to obtain rigidity results for Ricci flat manifolds, generalizing earlier work of Bando, Kasue and Nakajima.

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Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Ricci flat manifolds, weighted Sobolev inequalities, FOS: Mathematics, 46E35, 53C21 ; 53C25 ; 46E35, 53C21, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG], 53C25

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    influence
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citations
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!
33
Top 10%
Top 10%
Top 10%
Green
bronze