Geodesic
Recovering the metric of a $CAT(0)$-space by a diagonal tube
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 5-29
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Let $(x,d)$ be a locally compact geodesically complete $CAT(0)$-space of topological dimension $>1$. It is proved that if each geodesic segment in $X$ admits a unique continuation to a complete geodesic, then the metric $d$ is recovered by the diagonal tube $V\subset X\times X$ corresponding to an arbitrary $r>0$. This partly generalizes V. N. Berestovskii's results on A. D. Aleksandrov spaces of negative curvature. 
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P. D. Andreev. Recovering the metric of a $CAT(0)$-space by a diagonal tube. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 5-29. http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a0/

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