Smirnov Decomposition of a Horizontal Vector Charge in the Heisenberg Group
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914561159856128 |
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| author | Huang, Zhengyao Klingenberg, Wilhelm |
| author_facet | Huang, Zhengyao Klingenberg, Wilhelm |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_12716 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smirnov Decomposition of a Horizontal Vector Charge in the Heisenberg Group Huang, Zhengyao Klingenberg, Wilhelm Functional Analysis Classical Analysis and ODEs 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. |
| title | Smirnov Decomposition of a Horizontal Vector Charge in the Heisenberg Group |
| topic | Functional Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2605.12716 |