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2000 Existence results on prescribing zero scalar curvature
Qi S. Zhang, Z. Zhao
Differential Integral Equations 13(4-6): 779-790 (2000).


We study some time independent Schrödinger equations on complete noncompact manifolds. By showing that these equations have global positive solutions bounded away from zero, we prove that a large class of manifolds are conformal to complete manifolds with zero scalar curvature. They include those with Ricci curvature being nonnegative and the scalar curvature satisfying $V(x) \le C/d^{2}(x, x_{0})$ for an arbitrary $C>0$. As we have shown that there are noncompact manifolds with positive scalar curvature, which are not conformal to manifolds with positive constant scalar curvature, the issue of prescribing zero scalar curvature becomes interesting. The current result gives a partial answer to the Yamabe problem on noncompact manifolds with nonnegative Ricci curvatures.


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Qi S. Zhang. Z. Zhao. "Existence results on prescribing zero scalar curvature." Differential Integral Equations 13 (4-6) 779 - 790, 2000.


Published: 2000
First available in Project Euclid: 21 December 2012

zbMATH: 0990.53036
MathSciNet: MR1750050

Primary: 53C21
Secondary: 58J60

Rights: Copyright © 2000 Khayyam Publishing, Inc.


Vol.13 • No. 4-6 • 2000
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