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.
Singular Yamabe metrics by equivariant reduction / Hyder, A.; Pistoia, A.; Sire, Y.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 31:12(2021), pp. 12525-12547. [10.1007/s12220-021-00726-w]
Singular Yamabe metrics by equivariant reduction
Pistoia A.
;
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.File allegati a questo prodotto
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