Regularity of convex functions on Heisenberg groups
Zoltán M. Balogh, Matthieu Rickly (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.