Blow-up examples for the Yamabe problem

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Abstract

It has been conjectured that if solutions to the Yamabe PDE on a smooth Riemannian manifold (Mn, g) blow-up at a point p M, then all derivatives of the Weyl tensor Wg of g, of order less than or equal to, vanish at p M. In this paper, we will construct smooth counterexamples to the Weyl Vanishing Conjecture for any n ≥ 25.

Original languageEnglish (US)
Pages (from-to)377-397
Number of pages21
JournalCalculus of Variations and Partial Differential Equations
Volume36
Issue number3
DOIs
StatePublished - Oct 1 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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