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Nonexistence and uniqueness of positive solutions of Yamabe type equations on nonpositively curved manifolds

We prove nonexistence and uniqueness of positive C^{2} --solutions of the elliptic equation \Delta u +a(x)u - K(x)u^{\sigma }=0 , \sigma >1, on a nonpositively curved, complete manifold (M,g) .

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 1997-12, Vol.349 (12), p.4753-4774
Main Authors: Bianchini, Bruno, Rigoli, Marco
Format: Article
Language:English
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Summary:We prove nonexistence and uniqueness of positive C^{2} --solutions of the elliptic equation \Delta u +a(x)u - K(x)u^{\sigma }=0 , \sigma >1, on a nonpositively curved, complete manifold (M,g) .
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-97-01810-2