Blow-up phenomena for the Yamabe equation
Differential Geometry
2009-05-26 v1 Analysis of PDEs
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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Cite
@article{arxiv.0905.3840,
title = {Blow-up phenomena for the Yamabe equation},
author = {S. Brendle},
journal= {arXiv preprint arXiv:0905.3840},
year = {2009}
}
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Published paper