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.

中文翻译：

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通过等变约简的奇异 Yamabe 度量

我们使用等变设置中的问题的约简来构造 Yamabe 方程的奇异解。这提供了一个重要的几何示例，其分析比在 Mazzeo-Pacard 程序中更简单。我们的构造还提供了一个非平凡的例子，说明了涉及具有（平滑）系数的方程的 Yamabe 问题的弱解。