$C^{1,α}$-rectifiability in low codimension in Heisenberg groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866913577438281728 |
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| author | Idu, Kennedy Obinna Maiale, Francesco Paolo |
| author_facet | Idu, Kennedy Obinna Maiale, Francesco Paolo |
| contents | A natural notion of higher order rectifiability is introduced for subsets of Heisenberg groups $\mathbb{H}^n$ in terms of covering a set almost everywhere by a countable union of $(\mathbf{C}_H^{1,α},\mathbb{H})$-regular surfaces, for some $0 < α\leq 1$. We prove that a sufficient condition for $C^{1,α}$-rectifiability of low-codimensional subsets in Heisenberg groups is the almost everywhere existence of suitable approximate tangent paraboloids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_05165 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | $C^{1,α}$-rectifiability in low codimension in Heisenberg groups Idu, Kennedy Obinna Maiale, Francesco Paolo Metric Geometry Differential Geometry 28A75 (primary) 43A80, 53C17 (secondary) A natural notion of higher order rectifiability is introduced for subsets of Heisenberg groups $\mathbb{H}^n$ in terms of covering a set almost everywhere by a countable union of $(\mathbf{C}_H^{1,α},\mathbb{H})$-regular surfaces, for some $0 < α\leq 1$. We prove that a sufficient condition for $C^{1,α}$-rectifiability of low-codimensional subsets in Heisenberg groups is the almost everywhere existence of suitable approximate tangent paraboloids. |
| title | $C^{1,α}$-rectifiability in low codimension in Heisenberg groups |
| topic | Metric Geometry Differential Geometry 28A75 (primary) 43A80, 53C17 (secondary) |
| url | https://arxiv.org/abs/2102.05165 |