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

Tapio Rajala ^[1]
1. [1] University of Jyväskylä
  
  University of Jyväskylä
  
  Jyväskylä, Finlandia
Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 15, Nº Extra 1 (Special volume), 2016, págs. 45-68
Idioma: inglés
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Resumen
- 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.