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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.17600 |
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| _version_ | 1866915836031139840 |
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| author | Bouafia, Philippe |
| author_facet | Bouafia, Philippe |
| contents | We introduce a complex of cochains, $α$-fractional charges ($0 < α\leq 1$), whose regularity is between that of De Pauw-Moonens-Pfeffer's charges and that of Whitney's flat cochains. We show that $α$-Hölder differential forms and their exterior derivative can be realized as $α$-fractional charges, and that it is possible to define the exterior product between an $α$-fractional and a $β$-fractional charge, under the condition that $α+ β> 1$. This construction extends the Young integral in arbitrary dimension and codimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the exterior product of Hölder differential forms Bouafia, Philippe Differential Geometry We introduce a complex of cochains, $α$-fractional charges ($0 < α\leq 1$), whose regularity is between that of De Pauw-Moonens-Pfeffer's charges and that of Whitney's flat cochains. We show that $α$-Hölder differential forms and their exterior derivative can be realized as $α$-fractional charges, and that it is possible to define the exterior product between an $α$-fractional and a $β$-fractional charge, under the condition that $α+ β> 1$. This construction extends the Young integral in arbitrary dimension and codimension. |
| title | On the exterior product of Hölder differential forms |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2403.17600 |