Journal of Convex Analysis 26 (2019), No. 1, 001--014
Copyright Heldermann Verlag 2019
On Singular Sets of H-Monotone Maps
Zoltán M. Balogh
Mathematisches Institut, Universität Bern, Sidlerstr. 5, 3012 Bern, Switzerland
balogh.zoltan@math.unibe.ch
Valentina Penso
Mathematisches Institut, Universität Bern, Sidlerstr. 5, 3012 Bern, Switzerland
valentina.penso@math.unibe.ch
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, with values in R2n, is (2n+1-k, H)-rectifiable.
Keywords: Heisenberg group, H-monotonicity, singular set, convex functions.
MSC: 26B25, 49J53
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