Failure of the local-to-global property for CD(K,N) spaces

@inproceedings{Rajala2013FailureOT,
  title={Failure of the local-to-global property for CD(K,N) spaces},
  author={Tapio Rajala},
  year={2013}
}
Given any K 2 R and N 2 [1,1] we show that there exists a compact geodesic metric measure space satisfying locally the CD(0, 4) condition but failing to satisfy CD(K, N) globally. The space with this property is a suitable non-convex subset of R2 equipped with the l1-norm and the Lebesgue measure. Combining many such spaces gives a (non-compact) complete geodesic metric measure space satisfying CD(0, 4) locally but failing to satisfy CD(K, N) globally for every K and N. 

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