English

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.

Keywords

Cite

@article{arxiv.0905.3840,
  title  = {Blow-up phenomena for the Yamabe equation},
  author = {S. Brendle},
  journal= {arXiv preprint arXiv:0905.3840},
  year   = {2009}
}

Comments

Published paper

R2 v1 2026-06-21T13:05:19.534Z