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arXiv · 2403.17600

On the exterior product of H\"older differential forms

Philippe Bouafia
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Abstract

We introduce a complex of cochains, $\alpha$-fractional charges ($0 < \alpha \leq 1$), whose regularity is between that of De Pauw-Moonens-Pfeffer's charges and that of Whitney's flat cochains. We show that $\alpha$-H\"older differential forms and their exterior derivative can be realized as $\alpha$-fractional charges, and that it is possible to define the exterior product between an $\alpha$-fractional and a $\beta$-fractional charge, under the condition that $\alpha + \beta > 1$. This construction extends the Young integral in arbitrary dimension and codimension.

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Philippe Bouafia. 2024-03-26. On the exterior product of H\"older differential forms. https://arxiv.org/abs/2403.17600

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