Prescribing scalar curvatures on the conformal classes of complete metrics with negative curvature

Jin, Zhi Ren

doi:10.1090/S0002-9947-1993-1163364-0

Prescribing scalar curvatures on the conformal classes of complete metrics with negative curvature
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Trans. Amer. Math. Soc. 340 (1993), 785-810 Request permission

Abstract:

Let $({M^n},g)$ be a complete noncompact Riemannian manifold with the curvature bounded between two negative constants. Given a function $K$ on ${M^n}$, in terms of the behaviors of $K$ at infinite, we give a fairly complete answer to when the $K$ can be the scalar curvature function of a complete metric ${g_1}$ which is conformal to $g$.

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