  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.
