The tangent cone of an Aleksandrov space of curvature \(\leq K\) (Q1345751)
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scientific article; zbMATH DE number 733196
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The tangent cone of an Aleksandrov space of curvature \(\leq K\) |
scientific article; zbMATH DE number 733196 |
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The tangent cone of an Aleksandrov space of curvature \(\leq K\) (English)
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5 October 1995
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It is proved that for any Aleksandrov space of curvature bounded above (not necessarily geodesically complete or locally compact), the completed tangent cone at a point has nonpositive curvature (is a CAT(0) space). This fundamental theorem was originally proved by the same author under more restrictive hypotheses [the author, Sib. Math. J. 19, 944-949 (1979); translation from Sib. Mat. Zh. 19, 1341-1348 (1978; Zbl 0405.53044)].
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bounded curvature
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Aleksandrov space
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tangent cone
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