On the existence of deformations without critical points (the Teissier problem for functions of two variables) (Q1392315)

The main result asserts that if \(f:(\mathbb{C}^2,0) \to(\mathbb{C},0)\) is a real analytic germ with an isolated critical point at the origin and that the zero level curve \(\{f=0\}\subset(\mathbb{C}^2,0)\) has a single real component, then there exists a real deformation \(\widetilde f\) of \(f\) without real critical points.