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Alexandrov’s spaces with curvatures bounded from below II
- Publisher
- Wiley
- Copyright
- © 2018 London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms.12186
- Publisher site
- See Article on Publisher Site
Abstract
Perelman's doubling theorem asserts that the metric space obtained by gluing along their boundaries two copies of an Alexandrov space with curvature ⩾κ is an Alexandrov space with the same dimension and satisfying the same curvature lower bound. We show that this result cannot be extended to metric measure spaces satisfying synthetic Ricci curvature bounds in the MCP sense. The counterexample is given by the Grushin half‐plane, which satisfies the MCP (0,N) if and only if N⩾4, while its double satisfies the MCP (0,N) if and only if N⩾5.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Oct 1, 2018
Keywords: ; ;