Hölder continuous mappings, differential forms and the Heisenberg groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912555333582848 |
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| author | Hajłasz, Piotr Mirra, Jacob Schikorra, Armin |
| author_facet | Hajłasz, Piotr Mirra, Jacob Schikorra, Armin |
| contents | We develop analysis of Hölder continuous mappings with applications to geometry and topology of the Heisenberg groups. We cover the theory of distributional Jacobians of Hölder continuous mappings and pullbacks of differential forms under Hölder continuous mappings. That includes versions of the change of variables formula and the Stokes theorem for Hölder continuous mappings. The main applications are in the setting of the Heisenberg groups, where we provide a simple proof of a generalization of the Gromov non-embedding theorem, and new results about the Hölder homotopy groups of the Heisenberg groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hölder continuous mappings, differential forms and the Heisenberg groups Hajłasz, Piotr Mirra, Jacob Schikorra, Armin Differential Geometry Classical Analysis and ODEs Geometric Topology Primary: 26B35, 53C17, 53C23, 58A10, Secondary: 30L99, 55Q25, 55Q70, 58A14 We develop analysis of Hölder continuous mappings with applications to geometry and topology of the Heisenberg groups. We cover the theory of distributional Jacobians of Hölder continuous mappings and pullbacks of differential forms under Hölder continuous mappings. That includes versions of the change of variables formula and the Stokes theorem for Hölder continuous mappings. The main applications are in the setting of the Heisenberg groups, where we provide a simple proof of a generalization of the Gromov non-embedding theorem, and new results about the Hölder homotopy groups of the Heisenberg groups. |
| title | Hölder continuous mappings, differential forms and the Heisenberg groups |
| topic | Differential Geometry Classical Analysis and ODEs Geometric Topology Primary: 26B35, 53C17, 53C23, 58A10, Secondary: 30L99, 55Q25, 55Q70, 58A14 |
| url | https://arxiv.org/abs/2503.11506 |