We will show the Cheeger–Colding segment inequality for manifolds with integral Ricci curvature bound. By using this segment inequality, the almost rigidity structure results for integral Ricci curvature will be derived by a similar method as in [1]. And the sharp Hölder continuity result of [7] holds in the limit space of manifolds with integral Ricci curvature bound.

中文翻译：

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积分 Ricci 曲率的分段不等式和几乎刚性结构

我们将展示具有积分 Ricci 曲率界的流形的 Cheeger-Colding 段不等式。通过使用这种分段不等式，积分 Ricci 曲率的几乎刚性结构结果将通过与 [1] 中类似的方法得出。并且 [7] 的尖锐 Hölder 连续性结果在具有积分 Ricci 曲率界的流形的极限空间中成立。