, Volume 103, Issue 2, pp 169-182

On tangent cones of Alexandrov spaces with curvature bounded below

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Abstract:

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.

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