Blow-up phenomena for the Yamabe equation

Brendle, Simon

doi:10.1090/S0894-0347-07-00575-9

Blow-up phenomena for the Yamabe equation
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by Simon Brendle

J. Amer. Math. Soc. 21 (2008), 951-979

DOI: https://doi.org/10.1090/S0894-0347-07-00575-9

Published electronically: June 14, 2007

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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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