Symmetry and convexity of level sets of solutions to infinity Laplace's equation

We consider the Dirichlet problem $$displaylines{ -Delta_infty u=f(u) quad hbox{in }Omega,,cr u=0quad hbox{on }partialOmega,,} $$ where $Delta_infty u=u_{x_i}u_{x_j}u_{x_ix_j}$ and $f$ is a nonnegative continuous function. We investigate whether the solutions to this equation inherit geometrical properties from the domain $Omega$. We obtain results concerning convexity of level sets and symmetry of solutions.