Singular Yamabe metrics by equivariant reduction

TL;DR

This paper constructs singular solutions to the Yamabe equation through equivariant reduction, offering simpler analysis and new examples of weak solutions with smooth coefficients in geometric analysis.

Contribution

It introduces a novel equivariant reduction method to construct singular Yamabe metrics, simplifying analysis and providing new geometric examples.

Findings

Constructed explicit singular solutions to the Yamabe equation.

Provided a new class of weak solutions with smooth coefficients.

Simplified the analysis compared to previous approaches.

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.