We investigate the geometry of manifolds with bounded Ricci curvature in $L^1$-sense. In particular, we generalize the classical volume comparison theorem to our situation and obtain a generalized sphere theorem.

Keywords:

Mean curvature, Ricci curvature Mean curvature, Ricci curvature

MSC Classifications:

53C20 show english descriptions Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20]

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