On singular Yamabe obstructions

Abstract

We discuss the singular Yamabe obstruction ${\mathcal{B}}_3$ of a hypersurface in a four-dimensional general background. We derive various explicit formula for ${\mathcal{B}}_3$ from the original definition. We relate these formulas to corresponding formulas in the literature. The proofs are elementary.

arXiv comment33 pages, corrected typos, added reference

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• Residue families, singular Yamabe problems and extrinsic conformal Laplacians