Critical points of solutions of sub-elliptic equations on the Heisenberg group

Abstract This paper concerns the critical points of a class of degenerate elliptic operators. We prove that the nonexistence of critical point of the Green function for the Kohn-Laplacian of an H-star-shaped region on the first Heisenberg group. Moreover, we prove that solutions to a class of semi-linear degenerate elliptic equations on an H-star-shaped ring have no critical point.