RECOVERING THE METRIC OF A CAT(0)-SPACE BY A DIAGONAL TUBE


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Abstract

Let (x,d) be a locally compact geodesically complete CAT(0)-space of topological dimension greater than 1. It is proved that if each geodesic segment in X is uniquely extended to a complete geodesic, then the metric d is determined by the diagonal tube V ⊂ X × X corresponding to an arbitrary positive r. This partly generalizes V. N. Berestovskii's results on A. D. Aleksandrov spaces of negative curvature. Bibliography: 8 titles.

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