Abstract

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 Hn\mathbb{H}^n, with values in R2n\mathbb{R}^{2n}, is (2n+1−k,H)(2n+1-k, \mathbb{H})-rectifiable.

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Keywords

  • Heisenberg group
  • H-monotonicity
  • singular set
  • convex functions

Mathematics Subject Classification

26B25, 49J53

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Suggested citation

Z. M. Balogh, V. Penso. “On Singular Sets of H-Monotone Maps.” Journal of Convex Analysis 26 (2019), No. 1, 1–14. https://doi.org/10.68381/jca26001

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.