Horizontal normal map on the Heisenberg group

Abstract

We investigate the notion of H-subdifferential and H-normal map of a function on the Heisenberg group, based on its sub-Riemannian structure. In particular, a characterization of the convexity of a function is given via the nonemptiness of the H-subdifferential at every point.

Cited by in corpus (5)

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• On the $\mathbb{H}$-cone-functions for H-convex sets
• Differential games and Hamilton-Jacobi equations in the Heisenberg group
• Note on the Fenchel transform in the Heisenberg group