C1,α-rectifiability in low codimension in Heisenberg groups
A natural higher-order notion of C1,α{C}^{1,\alpha }-rectifiability, 0<α≤10\lt \alpha \le 1, is introduced for subsets of the Heisenberg groups Hn{{\mathbb{H}}}^{n} in terms of covering a set almost everywhere with a countable union of (CH1,α,H)\left({{\bf{C}}}_{H}^{1,\alpha },{\mathbb{H}})-regul...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-02-01
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| Series: | Analysis and Geometry in Metric Spaces |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/agms-2023-0105 |
| _version_ | 1797294681410764800 |
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| author | Idu Kennedy Obinna Maiale Francesco Paolo |
| author_facet | Idu Kennedy Obinna Maiale Francesco Paolo |
| author_sort | Idu Kennedy Obinna |
| collection | DOAJ |
| description | A natural higher-order notion of C1,α{C}^{1,\alpha }-rectifiability, 0<α≤10\lt \alpha \le 1, is introduced for subsets of the Heisenberg groups Hn{{\mathbb{H}}}^{n} in terms of covering a set almost everywhere with a countable union of (CH1,α,H)\left({{\bf{C}}}_{H}^{1,\alpha },{\mathbb{H}})-regular surfaces. Using this, we prove a geometric characterization of C1,α{C}^{1,\alpha }-rectifiable sets of low codimension in Heisenberg groups Hn{{\mathbb{H}}}^{n} in terms of an almost everywhere existence of suitable approximate tangent paraboloids. |
| first_indexed | 2024-03-07T21:34:45Z |
| format | Article |
| id | doaj.art-87c2dd51fea54509834380ce2a2e0ed6 |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-03-07T21:34:45Z |
| publishDate | 2024-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-87c2dd51fea54509834380ce2a2e0ed62024-02-26T14:28:00ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742024-02-0112152755510.1515/agms-2023-0105C1,α-rectifiability in low codimension in Heisenberg groupsIdu Kennedy Obinna0Maiale Francesco Paolo1Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, CanadaGran Sasso Science Institute, Viale F. Crispi 7, 67100 L’Aquila, ItalyA natural higher-order notion of C1,α{C}^{1,\alpha }-rectifiability, 0<α≤10\lt \alpha \le 1, is introduced for subsets of the Heisenberg groups Hn{{\mathbb{H}}}^{n} in terms of covering a set almost everywhere with a countable union of (CH1,α,H)\left({{\bf{C}}}_{H}^{1,\alpha },{\mathbb{H}})-regular surfaces. Using this, we prove a geometric characterization of C1,α{C}^{1,\alpha }-rectifiable sets of low codimension in Heisenberg groups Hn{{\mathbb{H}}}^{n} in terms of an almost everywhere existence of suitable approximate tangent paraboloids.https://doi.org/10.1515/agms-2023-0105higher orderapproximate tangent paraboloidsmetric spaces28a75 (primary)43a8053c17 (secondary) |
| spellingShingle | Idu Kennedy Obinna Maiale Francesco Paolo C1,α-rectifiability in low codimension in Heisenberg groups Analysis and Geometry in Metric Spaces higher order approximate tangent paraboloids metric spaces 28a75 (primary) 43a80 53c17 (secondary) |
| title | C1,α-rectifiability in low codimension in Heisenberg groups |
| title_full | C1,α-rectifiability in low codimension in Heisenberg groups |
| title_fullStr | C1,α-rectifiability in low codimension in Heisenberg groups |
| title_full_unstemmed | C1,α-rectifiability in low codimension in Heisenberg groups |
| title_short | C1,α-rectifiability in low codimension in Heisenberg groups |
| title_sort | c1 α rectifiability in low codimension in heisenberg groups |
| topic | higher order approximate tangent paraboloids metric spaces 28a75 (primary) 43a80 53c17 (secondary) |
| url | https://doi.org/10.1515/agms-2023-0105 |
| work_keys_str_mv | AT idukennedyobinna c1arectifiabilityinlowcodimensioninheisenberggroups AT maialefrancescopaolo c1arectifiabilityinlowcodimensioninheisenberggroups |