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

Bianchini, Bruno; Rigoli, Marco

doi:10.1090/S0002-9947-97-01810-2

Nonexistence and uniqueness of positive solutions of Yamabe type equations on nonpositively curved manifolds
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by Bruno Bianchini and Marco Rigoli

Trans. Amer. Math. Soc. 349 (1997), 4753-4774

DOI: https://doi.org/10.1090/S0002-9947-97-01810-2

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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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