Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Author: Zhi Ren Jin
Journal: Trans. Amer. Math. Soc. 340 (1993), 785-810
MSC: Primary 53C21; Secondary 35J60, 58G30
MathSciNet review: 1163364
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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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Keywords: Open complete Riemannian manifolds, scalar curvature, pointwise conformal change of metrics, nonexistence of solutions of an elliptic equation, subsolution, supersolution, completeness
Article copyright: © Copyright 1993 American Mathematical Society