On the horizontal Mean Curvature Flow for Axisymmetric surfaces in the   Heisenberg Group
  We study the horizontal mean curvature flow in the Heisenberg group by using the level-set method. We prove the uniqueness, existence and stability of axisymmetric viscosity solutions of the level-set equation. An explicit solution is given for the motion starting from a subelliptic sphere. We also give several properties of the level-set method and the mean curvature flow in the Heisenberg group. 
Fausto Ferrari, Qing Liu, Juan J. Manfredi
math.AP