A direct proof shows that a divergence-free horizontal vector current in the Heisenberg group decomposes as a measure on horizontal curves via the horizontal Liouville theorem.
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Smirnov Decomposition of a Horizontal Vector Charge in the Heisenberg Group
A direct proof shows that a divergence-free horizontal vector current in the Heisenberg group decomposes as a measure on horizontal curves via the horizontal Liouville theorem.