Flat compactness of normal currents, and charges in Carnot groups
Differential Geometry
2023-03-06 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.2303.02012,
title = {Flat compactness of normal currents, and charges in Carnot groups},
author = {Antoine Julia and Pierre Pansu},
journal= {arXiv preprint arXiv:2303.02012},
year = {2023}
}
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13 pages