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arXiv · 1506.02949

On dimensions of tangent cones in limit spaces with lower Ricci curvature bounds

Vitali Kapovitch·Nan Li
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Abstract

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 H\"older continuous with respect to measured Gromov-Hausdorff topology and have the same dimension in the sense of Colding-Naber.

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Vitali Kapovitch, Nan Li. 2015-06-09. On dimensions of tangent cones in limit spaces with lower Ricci curvature bounds. https://arxiv.org/abs/1506.02949

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