Abstract
We solve the well-known problem by A. D. Alexandrov for nonpositively curved spaces. Let X be a geodesically complete locally compact space nonpositively curved in the sense of Alexandrov and connected at infinity. The main theorem reads as follows: Each bijection f : X → X such that f and the inverse f −1 of f preserve distance 1 is an isometry of X.
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The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00315).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 3–24, January–February, 2006.
Original Russian Text Copyright © 2006 Andreev P. D.
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Andreev, P.D. A. D. Alexandrov's Problem for CAT(0)-Spaces. Sib Math J 47, 1–17 (2006). https://doi.org/10.1007/s11202-006-0001-1
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DOI: https://doi.org/10.1007/s11202-006-0001-1