The isoperimetric inequality in ℍ with respect to the horizontal perimeter was first proved by Pansu. We first state it in the setting of C1 sets.
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The isoperimetric inequality in ℍ. (2007). In Progress in Mathematics (Vol. 259, pp. 143–150). Springer Basel. https://doi.org/10.1007/978-3-7643-8133-2_7
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