Regularity of convex functions on Heisenberg groups

Annali della Scuola Normale Superiore di Pisa- Classe di Scienze 2 (4):847-868 (2003)
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Abstract

We discuss differentiability properties of convex functions on Heisenberg groups. We show that the notions of horizontal convexity and viscosity convexity are equivalent and that h-convex functions are locally Lipschitz continuous. Finally we exhibit Weierstrass-type h-convex functions which are nowhere differentiable in the vertical direction on a dense set or on a Cantor set of vertical lines

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