On the Density Problem in Heisenberg Rectifiability
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911144025784320 |
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| author | Idu, Kennedy Obinna |
| author_facet | Idu, Kennedy Obinna |
| contents | We resolve a problem posed by Mattila, Serapioni and Serra Cassano concerning the role of density assumptions in the characterization of rectifiable sets of low codimension in Heisenberg groups. Specifically, we prove that the positive lower density condition is not required: rectifiability is completely determined by the geometric property of almost everywhere existence of approximate tangent subgroups. This provides a simplified and intrinsic criterion for rectifiable sets in the subRiemannian setting and sharpens the analogy with Federer's classical Euclidean theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07212 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Density Problem in Heisenberg Rectifiability Idu, Kennedy Obinna Metric Geometry 28A75 (primary), 43A80, 53C17 (secondary) We resolve a problem posed by Mattila, Serapioni and Serra Cassano concerning the role of density assumptions in the characterization of rectifiable sets of low codimension in Heisenberg groups. Specifically, we prove that the positive lower density condition is not required: rectifiability is completely determined by the geometric property of almost everywhere existence of approximate tangent subgroups. This provides a simplified and intrinsic criterion for rectifiable sets in the subRiemannian setting and sharpens the analogy with Federer's classical Euclidean theorem. |
| title | On the Density Problem in Heisenberg Rectifiability |
| topic | Metric Geometry 28A75 (primary), 43A80, 53C17 (secondary) |
| url | https://arxiv.org/abs/2509.07212 |