A characterization of isometries of CAT(0)-space as maps preserving diagonal tube

Details A characterization of isometries of CAT(0)-space as maps preserving diagonal tube A characterization of isometries of CAT(0)-space as maps preserving diagonal tube

2003-08-11

arxiv.org/abs/math/0308096v2

Mathematics

Geometric Topology

28 pages

Scientific paper

We give positive answers for questions by Berestovskii. Namely, we prove that every bijection of locally compact geodesically complete and connected at infinity CAT(0)-space $X$ onto itself preserving some fixed distance or satellite relations is an isometry of this space. The proof of this theorem is based on another result stated by Berestovskii as a problem: the metric of the space $X$ may be recovered from its diagonal tube corresponding to an arbitrary number $r > 0$.

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