We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature bounded below and diameter bounded above, Gromov-Hausdorff convergence agrees with intrinsic flat convergence. In particular, the limiting current is essentially unique, has multiplicity one, and mass equal to the Hausdorff measure. Moreover, the limit spaces satisfy a constancy theorem.

中文翻译：

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流形的内在平坦和Gromov-Hausdorff收敛，Ricci曲率在下面。

我们表明，对于一个封闭的，连接的，定向的黎曼流形的非塌陷序列，其Ricci曲率限制在下面，直径限制在上面，Gromov-Hausdorff收敛与固有平坦收敛一致。特别是，极限电流本质上是唯一的，具有多重性1，质量等于Hausdorff量度。此外，极限空间满足常数定理。