Gromov-Hausdorff and intrinsic flat convergence of RCD(K,N) and Kato spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918321046159360 |
|---|---|
| author | Mondino, Andrea Perales, Raquel |
| author_facet | Mondino, Andrea Perales, Raquel |
| contents | We consider metric measure spaces $(X,\mathsf{d},\mathscr{H}^N)$ satisfying the properties (ETR), (LBD), and with an almost everywhere connected regular set. In particular, these assumptions are fulfilled 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03280 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gromov-Hausdorff and intrinsic flat convergence of RCD(K,N) and Kato spaces Mondino, Andrea Perales, Raquel Differential Geometry Metric Geometry We consider metric measure spaces $(X,\mathsf{d},\mathscr{H}^N)$ satisfying the properties (ETR), (LBD), and with an almost everywhere connected regular set. In particular, these assumptions are fulfilled 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. |
| title | Gromov-Hausdorff and intrinsic flat convergence of RCD(K,N) and Kato spaces |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2602.03280 |