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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Blow-up phenomena for the Yamabe equation


Author: Simon Brendle
Journal: J. Amer. Math. Soc. 21 (2008), 951-979
MSC (2000): Primary 53C21; Secondary 53C44
Published electronically: June 14, 2007
MathSciNet review: 2425176
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Abstract: Let $ (M,g)$ be a compact Riemannian manifold of dimension $ n \geq 3$. A well-known conjecture states that the set of constant scalar curvature metrics in the conformal class of $ g$ is compact unless $ (M,g)$ is conformally equivalent to the round sphere. In this paper, we construct counterexamples to this conjecture in dimensions $ n \geq 52$.


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Additional Information

Simon Brendle
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305

DOI: http://dx.doi.org/10.1090/S0894-0347-07-00575-9
PII: S 0894-0347(07)00575-9
Keywords: Scalar curvature, conformal deformation of Riemannian metrics, blow-up analysis
Received by editor(s): October 23, 2006
Published electronically: June 14, 2007
Additional Notes: This project was supported by the Alfred P. Sloan Foundation and by the National Science Foundation under grant DMS-0605223.
Article copyright: © Copyright 2007 American Mathematical Society