3 problems

Let $\varphi$ be plurisubharmonic in a bounded pseudoconvex neighborhood of $0\in\mathbb{C}^n$, locally bounded away from $0$. For $m\in\mathbb{Z}_{>0}$, let $\varphi_m$ be the ana…

Let $\varphi$ and $\psi$ be plurisubharmonic germs with isolated singularities at $0\in\mathbb{C}^n$. For every divisorial valuation $v$ centered at $0$, write $v(\varphi)$ for its…

Valuative invariance conjecture. If $\varphi$ and $\psi$ are valuatively equivalent, then their $n$-th Lelong numbers at $0$ are equal: