2 problems

Let $D$ be a Stein domain in $\mathbb C^n$, and let its Bergman space be the space of holomorphic functions on $D$ that belong to $L^2(D)$ with respect to Lebesgue measure. Wiegeri…

Gompf's conjecture. No nontrivial Brieskorn sphere, with either orientation, arises as the boundary of a Stein domain in $\mathbb{C}^2$.