The subelliptic heat kernel on SU(2): Representations, Asymptotics and   Gradient bounds
  The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities. 
Fabrice Baudoin, Michel Bonnefont