Abstract
We establish some Boju–Funar type compactness criteria for complete Riemannian manifolds via [Formula: see text]-Bakry–Émery and [Formula: see text]-modified Ricci curvatures assuming that [Formula: see text]-Bakry–Émery and [Formula: see text]-modified Ricci curvatures tend slowly to zero as the distance from a fixed point goes to infinity. Our results are generalizations of Cheeger–Gromov–Taylor type compactness criteria for complete Riemannian manifolds via [Formula: see text]-Bakry–Émery and [Formula: see text]-modified Ricci curvatures established by Y. Soylu and the author.
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