Blow-up examples for the Yamabe problem

Marques, Fernando C.
November 2009
Calculus of Variations & Partial Differential Equations;Nov2009, Vol. 36 Issue 3, p377
Academic Journal
It has been conjectured that if solutions to the Yamabe PDE on a smooth Riemannian manifold ( M n, g) blow-up at a point $${p \in M}$$ , then all derivatives of the Weyl tensor W g of g, of order less than or equal to $${[\frac{n-6}{2}]}$$ , vanish at $${p \in M}$$ . In this paper, we will construct smooth counterexamples to the Weyl Vanishing Conjecture for any n ≥ 25.


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