English

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}
}

Comments

13 pages

R2 v1 2026-06-28T08:59:54.513Z