Ohsawa's Bergman-kernel restriction conjecture

Let $M$ be a Stein manifold of complex dimension $n$, let $S$ be a closed complex submanifold, and let $G(,S)$ be the upper envelope of the polar functions associated with $S$. Let $b4b4_M$ and $b4b4_{M/S}$ denote the Bergman kernels of $M$ and $S$ defined from complete orthogonal systems of the corresponding $L^2$ holomorphic canonical sections. If $S_{n-k}$ is the $n-k$-dimensional component of $S$, then Ohsawa's conjecture.

$$\frac{\pi^k}{k!}\kappa_M(x)\ge\kappa_{M/S}(x)$$

for any $x\in S_{n-k}$. The conjecture was proved by Guan and Zhou, so the inequality is no longer open.