Segment inequality and almost rigidity structures for integral Ricci curvature
Abstract
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 CC1. And the sharp H\"older continuity result of CoN holds in the limit space of manifolds with integral Ricci curvature bound.
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