## Blow-up phenomena for the Yamabe equation

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- by Simon Brendle PDF
- J. Amer. Math. Soc.
**21**(2008), 951-979 Request permission

## 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 $n \geq 52$.## References

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## Additional Information

**Simon Brendle**- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
- MR Author ID: 655348
- 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.
- © Copyright 2007 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**21**(2008), 951-979 - MSC (2000): Primary 53C21; Secondary 53C44
- DOI: https://doi.org/10.1090/S0894-0347-07-00575-9
- MathSciNet review: 2425176