Regularity estimates for convex functions in Carnot-Carath\'eodory   spaces
  We prove some regularity estimates for a class of convex functions in Carnot-Carath\'eodory spaces, generated by H\"ormander vector fields. Our approach relies on both the structure of metric balls induced by H\"ormander vector fields and local upper estimates for the corresponding subharmonic functions. 
Valentino Magnani and Matteo Scienza
math.AP