Submitted Paper

Inserted: 21 feb 2026
Last Updated: 21 feb 2026

Year: 2026

Abstract:

We consider metric measure spaces satisfying the curvature-free properties (ETR), (LDB), and with an almost everywhere connected regular set. In particular, these assumptions are satisfied by non-collapsed RCD(K,N) spaces without boundary, as well as by non-collapsed strong Kato limit spaces without boundary. For both classes, we study orientability in the sense of metric currents, establish stability of orientation under pointed Gromov-Hausdorff convergence, and show that the pointed Gromov-Hausdorff limit coincides with the local flat limit.

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• RCD_IFequalsGH-3.pdf