A minimal regularity for the area formula in the Engel group
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908801067646976 |
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| author | Corni, Francesca Essebei, Fares Magnani, Valentino |
| author_facet | Corni, Francesca Essebei, Fares Magnani, Valentino |
| contents | We prove that the upper blow-up theorem in the Engel group holds for $C^1$ submanifolds. Combining this result with the known negligibility of the singular set, we obtain an integral representation of the spherical measure for all surfaces of class $C^{1,α}$ in the Engel group. A new and central aspect of our method is the suitable use of Stokes' theorem to prove the upper blow-up, which relies on the special algebraic structure of left-invariant forms in the Engel group. Some general tools are also introduced to establish area formulas in arbitrary stratified group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00346 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A minimal regularity for the area formula in the Engel group Corni, Francesca Essebei, Fares Magnani, Valentino Metric Geometry We prove that the upper blow-up theorem in the Engel group holds for $C^1$ submanifolds. Combining this result with the known negligibility of the singular set, we obtain an integral representation of the spherical measure for all surfaces of class $C^{1,α}$ in the Engel group. A new and central aspect of our method is the suitable use of Stokes' theorem to prove the upper blow-up, which relies on the special algebraic structure of left-invariant forms in the Engel group. Some general tools are also introduced to establish area formulas in arbitrary stratified group. |
| title | A minimal regularity for the area formula in the Engel group |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2602.00346 |