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            Abstract A version of the singular Yamabe problem in smooth domains in a closed manifoldyields complete conformal metrics with negative constant scalar curvatures.In this paper, we study the blow-up phenomena of Ricci curvatures of these metrics on domains whose boundary is close to a certain limit set of a lower dimension.We will characterize the blow-up set according to the Yamabe invariant of the underlying manifold.In particular, we will prove that all points in the lower dimension part of the limit set belong to the blow-up set on manifolds not conformally equivalent to the standard sphere and that all but one point in the lower dimension part of the limit set belong to the blow-up set on manifolds conformally equivalent to the standard sphere.In certain cases, the blow-up set can be the entire manifold.We will demonstrate by examples that these results are optimal.more » « lessFree, publicly-accessible full text available March 28, 2026
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