Published Paper

Inserted: 5 jun 2003
Last Updated: 27 apr 2004

Journal: Ann. Scuola Norm. Sup. Pisa
Volume: II
Number: 5
Pages: 847-868
Year: 2003

Abstract:

We discuss differentiability properties of convex functions on Heisenberg groups. We show that the notions of horizontal convexity (h-convexity) and viscosity convexity (v-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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