Metrics of constant scalar curvature conformal to Riemannian products
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- Proc. Amer. Math. Soc. 138 (2010), 2897-2905 Request permission
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 $\lambda$.References
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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
- MR Author ID: 626122
- Email: jimmy@cimat.mx
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2897-2905
- MSC (2010): Primary 53C21
- DOI: https://doi.org/10.1090/S0002-9939-10-10293-7
- MathSciNet review: 2644902