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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.01373 |
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| _version_ | 1866912256083623936 |
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| author | Alberti, Giovanni Massaccesi, Annalisa Merlo, Andrea |
| author_facet | Alberti, Giovanni Massaccesi, Annalisa Merlo, Andrea |
| contents | In this paper, we establish refined versions of the Frobenius Theorem for non-involutive distributions and use these refinements to prove an unrectifiability result for Carnot-Carathéodory spaces. We also introduce a new class of metric spaces that extends the framework of Carnot-Carathéodory geometry and show that, within this class, Carnot-Carathéodory spaces are, in some sense, extremal. Our results provide new insights into the relationship between integrability, non-involutivity, and rectifiability in both classical and sub-Riemannian settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01373 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tangency sets of non-involutive distributions and unrectifiability in Carnot-Carathéodory spaces Alberti, Giovanni Massaccesi, Annalisa Merlo, Andrea Differential Geometry Functional Analysis Metric Geometry 58A30, 53C17, 58A25, 35R03 In this paper, we establish refined versions of the Frobenius Theorem for non-involutive distributions and use these refinements to prove an unrectifiability result for Carnot-Carathéodory spaces. We also introduce a new class of metric spaces that extends the framework of Carnot-Carathéodory geometry and show that, within this class, Carnot-Carathéodory spaces are, in some sense, extremal. Our results provide new insights into the relationship between integrability, non-involutivity, and rectifiability in both classical and sub-Riemannian settings. |
| title | Tangency sets of non-involutive distributions and unrectifiability in Carnot-Carathéodory spaces |
| topic | Differential Geometry Functional Analysis Metric Geometry 58A30, 53C17, 58A25, 35R03 |
| url | https://arxiv.org/abs/2503.01373 |