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Metrics of constant scalar curvature conformal to Riemannian products

Author: Jimmy Petean
Journal: Proc. Amer. Math. Soc. 138 (2010), 2897-2905
MSC (2010): Primary 53C21
Published electronically: March 29, 2010
MathSciNet review: 2644902
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Abstract: We consider the conformal class of the Riemannian product $ g_0 +g$, where $ g_0$ is the constant curvature metric on $ S^m$ and $ g$ is a metric of constant scalar curvature on some closed manifold. We show that the number of metrics of constant scalar curvature in the conformal class grows at least linearly with respect to the square root of the scalar curvature of $ g$. This is obtained by studying radial solutions of the equation $ \Delta u -\lambda u + \lambda u^p =0$ on $ S^m$ and the number of solutions in terms of $ \lambda$.

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Additional Information

Jimmy Petean
Affiliation: Centro de Investigación en Matemáticas, A.P. 402, 36000, Guanajuato, Guanajuato, México – and – Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina

Received by editor(s): January 26, 2009
Received by editor(s) in revised form: November 18, 2009
Published electronically: March 29, 2010
Additional Notes: The author was supported by grant 106923-F of CONACYT
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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