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Asymptotic rigidity of Hadamard 2-spaces. (English) Zbl 0984.53014

Locally compact, geodesically complete 2-dimensional Hadamard spaces whose Tits ideal boundaries have the minimal diameter equal to \( \pi \), are classified. Moreover, the author gives a classification of the universal covering spaces of certain 2-dimensional nonpositively curved spaces. This is an extension of the result obtained in the polyhedral case by W. Ballmann and M. Brin [Publ. Math., Inst. Hautes Étud. Sci. 82, 169-209 (1995; Zbl 0866.53029)] and by S. Barré [Ann. Inst. Fourier 45, No. 4, 1037-1059 (1995; Zbl 0831.53031)].

MSC:

53C20 Global Riemannian geometry, including pinching
53C22 Geodesics in global differential geometry
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