4 problems

Bergman density rigidity conjecture. Then $\Phi$ is either holomorphic and

Let $m>n$ be positive integers with $\gcd(m,n)=1$, and let $Q_{m,n}$ be the degree $2m-2n$ palindromic polynomial associated with this pair. Write…

Let $\Omega$ be an open Riemann surface admitting a nontrivial Green function $G_{\Omega}$. For $z_0\in\Omega$, let $c_{\beta}(z_0)$ denote its logarithmic capacity and let…

Monotonicity conjecture. If $\Omega$ is pseudoconvex in $\mathbb C^n$ then this function is non-decreasing on $(-\infty,0]$. The conjecture is proved in dimension one; in arbitrary di…