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A. D. ALEXANDROV’S PROBLEM FOR BUSEMANN NON-POSITIVELY CURVED SPACES

By P. D. Andreev

Abstract

Abstract. The paper is the last in the cycle devoted to the solution of Alexandrov’s problem for nonpositively curved spaces. Here we study non-positively curved spaces in the sense of Busemann. We prove that if X is geodesically complete connected at infinity proper Busemann space, then it has the following characterization of isometries. For any bijection f: X → X, if f and f −1 preserve the distance 1, then f is an isometry

Topics: Busemann non-positive curvature, isometry, r-sequence, geodesic boundary, horofunction boundary Contents
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