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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

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

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