5 problems

Let $F$ be a holomorphic automorphism acting hyperbolically on a compact invariant set $K$, and let $W^s(K)$ be a stable manifold arising from this action. Stable-manifold Euclidea…

Intrinsic moduli-space conjecture. The proto-moduli spaces for $\operatorname{Aut}_{\operatorname{hol}}(\mathbb C^n)$ are actual moduli spaces when $n>1$ as well.

For $n\geq 2$, consider the complex algebraic torus $({\mathbb C}^*)^n$ and the density property, meaning that complete holomorphic vector fields generate the relevant holomorphic…

Fornaess–Stensønes basin conjecture. The basin $\Omega$ is always biholomorphic to $\mathbb C^m$. A positive answer would imply a positive answer to Bedford's stable-manifold conje…

Let $B$ be the unit ball in $\mathbb{C}^d$, and let $(f_n\colon B\to B)_{n\in\mathbb{N}}$ be a sequence of holomorphic maps fixing $0$ and satisfying … for some…