6 problems

Let $f(z,w)=(p(z),q(w))$ be the product of two polynomial maps of degree $d$ in $\mathbb{C}$. The non-density conjecture. If $p$ or $q$ belongs to the bifurcation locus in…

Let $M,M'\subset\mathbb{C}^n$, with $n\geq 2$, be globally minimal real analytic hypersurfaces. Let $h:M\to M'$ be a continuous CR mapping whose holomorphic extension to a global o…

Let $D,D'\subset\mathbb{C}^n$, with $n\geq 2$, be bounded domains whose boundaries are real analytic and geometrically smooth, and let $h:D\to D'$ be a proper holomorphic mapping.…

Let $M\subset\mathbb C^N$ be a real analytic CR submanifold, let $p\in M$ be a point of finite type, and let $K$ be a positive integer. Let $M'\subset\mathbb C^{N'}$ be a real anal…

Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be an injective holomorphic map germ. A map germ is corank $1$ when the differential $df_0$ has corank $1$. Lê's conjecture.…

Resolvent starlikeness conjecture. Every mapping $G_\lambda$ is starlike of order at least $\frac12$. Furthermore, the order of starlikeness of $G_\lambda$ tends to $1$ as…