On Singular Sets of H-Monotone Maps

The purpose of our paper is to extend a result of Alberti and Ambrosio about singularity sets of monotone multivalued maps to the sub-Riemmanian setting of Heisenberg groups. We prove that the k-th horizontal singular set of an H-monotone multivalued map of the Heisenberg group $\mathbb{H}^n$, with values in $\mathbb{R}^{2n}$, is $(2n+1-k, \mathbb{H})$-rectifiable.