1D symmetry for solutions of semilinear and quasilinear elliptic equations

Several new 1D results for solutions of possibly singular or degenerate elliptic equations, inspired by a conjecture of De Giorgi, are provided. In particular, 1D symmetry is proven under the assumption that either the profiles at infinity are 2D, or that one level set is a complete graph, or that the solution is minimal or, more generally, Q-minimal.