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arXiv · 0905.3840

Blow-up phenomena for the Yamabe equation

S. Brendle
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Abstract

Let (M,g) be a compact Riemannian manifold of dimension n \geq 3. The Compactness Conjecture asserts 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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S. Brendle. 2009-05-23. Blow-up phenomena for the Yamabe equation. https://arxiv.org/abs/0905.3840

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