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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Bruno Bianchini and Marco Rigoli
Journal: Trans. Amer. Math. Soc. 349 (1997), 4753-4774
MSC (1991): Primary 53C21, 58G03
MathSciNet review: 1401514
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Abstract | References | Similar Articles | Additional Information

Abstract: 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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Additional Information

Bruno Bianchini
Affiliation: B.B. e M.R. Dipartimento di Matematica, Universitá di Milano, Via Saldini, 50, 20133, Milano, Italy

Marco Rigoli
Affiliation: B.B. e M.R. Dipartimento di Matematica, Universitá di Milano, Via Saldini, 50, 20133, Milano, Italy
Email: rigoli@vmimat.mat.unimi.it

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01810-2
PII: S 0002-9947(97)01810-2
Keywords: Maximum principles, elliptic differential inequalities, Riemannian geometry
Received by editor(s): March 6, 1995
Article copyright: © Copyright 1997 American Mathematical Society