We find conditions under which the pretangent spaces to general metric spaces have the nonpositive Aleksandrov curvature or nonnegative one. The infinitesimal structure of general metric spaces with Busemann convex pretangent spaces is also described.
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Abdullayev, O. Dovgoshey, M.
Kucukaslan, Compactness and boundedness of tangent spaces to metric spaces, Beitr. Algebra Geom. Berg, I. Nikolaev, Quasilinearization and curvature of Aleksandrov spaces, Geom. Dedicata, , — Bilet, Geodesic tangent spaces to metric spaces, Ukr. Bilet, O.
Metric Spaces of Non-Positive Curvature | SpringerLink
Dovgoshey, Isometric embeddings of pretangent spaces in En, Bull. Simon Stevin. Dovgoshey, Metric betweenness, Ptolemaic spaces and isometric embeddings of pretangent spaces in R, J. On Toponogov's theorem for spaces of non positive curvature Ask Question.
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Viewed times. I have two questions: 1 Is the inverse implication of Thm 1 true if the inequality is verified for every triangle then the space has non positive curvature?
Metric Spaces of Non-Positive Curvature / Edition 1
Also can you give me a good reference on these Toponogov's theorems? Del 3, 1 1 gold badge 6 6 silver badges 24 24 bronze badges. Incidentally, I do not think Theorem 1 is due to Toponogov, I am nearly sure it is due to Alexadrov but maybe it was proven by Busemann or Rauch earlier : A.
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Schauder Fixed Point Theorem in Spaces with Global Nonpositive Curvature
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