Cheeger–Gromov–Taylor-type compactness theorems via integral radial m-Bakry–Émery Ricci curvatures

Source abstract

Inspired by the recent work of Wu, we extend the classical compactness theorem for complete Riemannian manifolds via Ricci curvature due to Cheeger, Gromov, and Taylor by replacing their asymptotic condition on the Ricci curvature by some upper bounds on integral radial m-Bakry–Émery Ricci curvatures when m is a positive constant, a negative constant, or infinity. Our results generalize the Cheeger–Gromov–Taylor-type compactness theorems for complete Riemannian manifolds via m-Bakry–Émery Ricci curvatures obtained by Soylu and the author to the case of integral settings.