Regularity of convex functions on Heisenberg groups

• Zoltán M. Balogh ^[1] ; Matthieu Rickly ^[1]
  1. [1] University of Bern

     University of Bern

     Bern/Berne/Berna, Suiza

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 2, Nº 4, 2003, págs. 847-868
• Idioma: inglés
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• Resumen

  • 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.