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Moduli spaces of singular Yamabe metrics. (English) Zbl 0849.58012
This paper considers the problem of determining the moduli space of complete, conformally flat metrics of constant positive scalar curvature on the complement of \(k\) points in \(S^n\). A Fredholm theory and asymptotic regularity theory for the Laplacian on asymptotically periodic manifolds is developed. It is shown that the moduli space is locally a real analytic variety of formal dimension \(k\): this is obtained by writing the space as the intersection of a Fredholm pair of real analytic manifolds.

MSC:
58D27 Moduli problems for differential geometric structures
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