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arXiv · 2605.12716

Smirnov Decomposition of a Horizontal Vector Charge in the Heisenberg Group

Zhengyao Huang·Wilhelm Klingenberg
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Abstract

A divergence-free horizontal vector current in Heisenberg space may be viewed as an element of the dual space of horizontal test vector fields. By applying a horizontal Liouville theorem in this setting, the flow lines of such a vector field generate a family of horizontal curves and an associated measure on this collection. In this paper, we provide a direct proof of the Smirnov decomposition for a Federer-Fleming current within the horizontal distribution.

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Zhengyao Huang, Wilhelm Klingenberg. 2026-05-12. Smirnov Decomposition of a Horizontal Vector Charge in the Heisenberg Group. https://arxiv.org/abs/2605.12716

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