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arXiv · 2511.18895

Currents in Heisenberg groups

Bruno Franchi·Pierre Pansu
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Abstract

There are three approaches to currents tuned to the anisotropic geometry of Heisenberg groups: Ambrosio and Kirchheim's approach valid for general metric spaces; distributions dual to horizontal differential forms; distributions dual to Rumin's complex. It is shown that, in dimensions less than half the ambient dimension, these three theories coincide. On the other hand, they diverge beyond middle dimension: Ambrosio-Kirchheim currents vanish, Rumin currents correspond to a new class of Federer-Fleming currents called oblique currents.

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Bruno Franchi, Pierre Pansu. 2025-11-24. Currents in Heisenberg groups. https://arxiv.org/abs/2511.18895

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