On dimensions of tangent cones in limit spaces with lower Ricci curvature bounds. (English) Zbl 1397.53054
Summary: We show that if \(X\) is a limit of \(n\)-dimensional Riemannian manifolds with Ricci curvature bounded below and \(\gamma\) is a limit geodesic in \(X\), then along the interior of \(\gamma\) same scale measure metric tangent cones \(T_{\gamma(t)}X\) are Hölder continuous with respect to measured Gromov-Hausdorff topology and have the same dimension in the sense of Colding-Naber.
MSC:
| 53C23 | Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces |
References:
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