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arXiv · 1207.3668

On Toponogov's comparison theorem for Alexandrov spaces

Urs Lang·Viktor Schroeder
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Abstract

In this expository note, we present a transparent proof of Toponogov's theorem for Alexandrov spaces in the general case, not assuming local compactness of the underlying metric space. More precisely, we show that if M is a complete geodesic metric space such that the Alexandrov triangle comparisons for curvature greater than or equal to k are satisfied locally, then these comparisons also hold in the large. The proof is a modification of an argument due to Plaut.

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Urs Lang, Viktor Schroeder. 2012-07-25. On Toponogov's comparison theorem for Alexandrov spaces. https://arxiv.org/abs/1207.3668

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