4 problems

Let $\mathbb B^n:=\{z\in\mathbb C^n:\|z\|<1\}$ be the unit ball, and let $F:\mathbb B^n\to\mathbb C^n$ be a univalent map with … Write $D:=F(\mathbb B^n)$ and suppose that $D$ is c…

Let $\mathbb{B}^n$ be the unit ball in $\mathbb{C}^n$, and let an inner function on $\mathbb{B}^n$ mean a bounded holomorphic function whose radial boundary values have modulus one…

Let $n\geq 3$, let $\mathbb{B}^n\subset\mathbb{R}^n$ be the unit ball with boundary sphere $\mathbb{S}^{n-1}$, and let $u\in C^{\infty}(\mathbb{B}^n)$ be positive and satisfy … whe…

Guo–Wang's conjecture. If $1<q<\frac{n}{n-2}$ and $0<\lambda\leq\frac{1}{q-1}$, then $u$ is constant.