1D symmetry for solutions of semilinear and quasilinear elliptic equations

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