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arXiv · 2303.02012

Flat compactness of normal currents, and charges in Carnot groups

Antoine Julia·Pierre Pansu
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Abstract

We prove that the family of normal currents in the sense of Rumin in a Carnot group is compact in the flat topology. This result is obtained through a dual compactness argument for Rumin forms, using the pseudo-differential calculus in groups developed by Folland, Christ-Geller-G lowacki-Polin and Rumin. As an application, imitating de Pauw-Moonens-Pfeffer, we describe the space of charges on a Carnot group.

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Antoine Julia, Pierre Pansu. 2023-03-03. Flat compactness of normal currents, and charges in Carnot groups. https://arxiv.org/abs/2303.02012

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