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

TL;DR

This paper proves a local-to-global property for the curvature-dimension condition in locally finite metric-measure spaces, extending previous work to a broader class of spaces with synthetic curvature bounds.

Contribution

It establishes the local-to-global property of the CD(K,N) condition for essentially non-branching, locally finite spaces, broadening the scope of synthetic curvature analysis.

Findings

Proves the local-to-global property for CD(K,N) in locally finite spaces.

Extends previous results to a wider class of metric-measure spaces.

Supports the analysis of curvature in more general geometric contexts.

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].