Singular Yamabe Metrics by Equivariant Reduction
The Journal of Geometric Analysis(2021)
Abstract
We construct singular solutions to the Yamabe equation using a reduction of the problem in an equivariant setting. This provides a non-trivial geometric example for which the analysis is simpler than in Mazzeo-Pacard program. Our construction provides also a non-trivial example of a weak solution to the Yamabe problem involving an equation with (smooth) coefficients.
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Key words
Singular solution,Yamabe problem,Warped product manifold,Equivariant solution
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