Theorem proves compactness in locally conformally flat Riemannian manifolds with specific curvature bounds, suggesting broader implications for geometry.
In this paper, we prove that if a complete locally conformally flat Riemannian manifold with positive Yamabe invariant has a positive lower bound on its scalar curvature, an upper bound on its Ricci curvature, and the Lq norm (q⩾2) of the traceless Ricci curvature is finite, then it is compact.
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Shunjuan Cao (2026) studied this question.
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