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

, with values in

\mathbb{R}^{2n} R 2 n

, is

(2n+1-k, \mathbb{H}) ( 2 n + 1 − k , H )

-rectifiable.