Blow-up phenomena for the Yamabe equation

Brendle, Simon ¹

¹ Department of Mathematics, Stanford University, Stanford, California 94305

Journal of the American Mathematical Society, Tome 21 (2008) no. 4, pp. 951-979

Résumé

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 $n \geq 52$.

Détail

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

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