The Globalization Theorem for CD(K,N) on locally finite Spaces

Abstract

We establish the local-to-global property of the synthetic curvature-dimension condition for essentially non-branching locally finite metric-measure spaces, extending the work [F. Cavalletti, E. Milman \textit{Invent. Math.} 226 (2021), no. 1, 1-137].

arXiv comment21 pages. The definition of CD^1(K,N) is changed to a more convenient one. The part on the implication from CD^1 to CD is extensively expanded