Semilinear PDEs in the Heisenberg group: The role of the right invariant vector fields Original Research Article

Some geometric features of the stable solutions of semilinear PDEs in the Heisenberg group are dealt with. A nonexistence result is given. The analysis is carried out by investigating the role of the right invariant vector fields: the monotonicity along these vector fields implies the stability of the solution and it naturally gives rise to geometrically interesting quantities.