On the second order derivatives of convex functions on the Heisenberg group

• Cristian E. Gutiérrez ^[1] ; Annamaria Montanari ^[2]
  1. [1] Temple University

     Temple University

     City of Philadelphia, Estados Unidos

     
  2. [2] University of Bologna

     University of Bologna

     Bolonia, Italia

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 3, Nº 2, 2004, págs. 349-366
• Idioma: inglés
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• Resumen

  • In the Euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous H–convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives for the class of continuous H–convex functions in the Heisenberg group.