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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Blow-up phenomena for the Yamabe equation
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by Simon Brendle PDF
J. Amer. Math. Soc. 21 (2008), 951-979 Request permission

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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Additional Information
  • Simon Brendle
  • Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
  • MR Author ID: 655348
  • Received by editor(s): October 23, 2006
  • Published electronically: June 14, 2007
  • Additional Notes: This project was supported by the Alfred P. Sloan Foundation and by the National Science Foundation under grant DMS-0605223.
  • © Copyright 2007 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 21 (2008), 951-979
  • MSC (2000): Primary 53C21; Secondary 53C44
  • DOI: https://doi.org/10.1090/S0894-0347-07-00575-9
  • MathSciNet review: 2425176