14 problems

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.…

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…

Baouendi–Rothschild–Zaitsev approximation conjecture. The holomorphic mapping $H$ with this approximation property should exist under these hypotheses. This would generalize the kn…

Let $D=G$ be very nice domains, specifically strongly pseudoconvex domains, without assuming simple connectivity, and let $F:D\to G$ be a holomorphic mapping with the real slice ri…

Let $D$ and $G$ be nice domains, and let $F:D\to G$ be a holomorphic mapping with the real slice rigidity property. Assume additionally that $D$ is simply connected. Simple-connect…

Let $D$ and $G$ be nice domains, for example bounded pseudoconvex domains, and let $F:D\to G$ be a holomorphic mapping with the real slice rigidity property. Real slice rigidity co…

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…

Linearity conjecture. Then $f$ must be linear. The conjecture concerns the exceptional singular-value condition in the classification of holomorphic $(2,1)$-subharmonic morphisms;…

Let $n>1$, let $N<2n-1$, and let $f$ be a proper holomorphic mapping from the unit ball … into … which is $C^2$-smooth up to the boundary. Cima–Suffridge conjecture. There exist au…

Let $D,D'\subset\mathbb C^n$ be bounded domains with real analytic boundaries, and let $f:D\to D'$ be a proper holomorphic map. Holomorphic extension conjecture. The map $f$ extend…

Let $D,G\subset\mathbb{C}^n$ be smoothly bounded pseudoconvex domains, and let $f:D\to G$ be a proper holomorphic mapping. Boundary smoothness conjecture. The map $f$ extends smoot…

Let $M$ and $M'$ be generic submanifolds of the same dimension in complex spaces, with $p\in M$, $H(M)\subset M'$, and $p'=H(p)$. Assume that $M$ is of finite type and essentially…