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

2013/05/28 by Rajala, Tapio
#28A33 #49Q20 (Secondary) #53C23 (Primary) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1305.6436

Abstract

Given any K and N we show that there exists a compact geodesic metric measure space satisfying locally the CD(0,4) condition but failing CD(K,N) globally. The space with this property is a suitable non convex subset of R² equipped with the l^∞-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 CD(K,N) globally for every K and N.

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