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On tangent cones of Alexandrov spaces with curvature bounded below

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The tangent cones of an inner metric Alexandrov space with finite Hausdorff dimension and a lower curvature bound are always inner metric spaces with nonnegative curvature. In this paper we construct an infinite-dimensional inner metric Alexandrov space of nonnegative curvature which has in one point a tangent cone whose metric is not an inner metric.

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Received: 20 October 1999 / Revised version: 8 May 2000

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Halbeisen, S. On tangent cones of Alexandrov spaces with curvature bounded below. manuscripta math. 103, 169–182 (2000). https://doi.org/10.1007/s002290070018

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  • DOI: https://doi.org/10.1007/s002290070018

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