Burns–Krantz conjecture for finite-type pseudoconvex domains

Let $\Omega \subset \mathbb{C}^d$ be a pseudoconvex domain of finite type and let $\xi_0 \in \partial \Omega$. A holomorphic self-map is a map $f:\Omega\to\Omega$ that is holomorphic. Burns–Krantz conjecture. There exists an integer $m$, depending on the geometry of $\partial\Omega$ at $\xi_0$, such that if

$$f(z)=z+o\left(\left\|z-\xi_0\right\|^m\right),$$

then $f=\operatorname{id}$. This asks whether finite type supplies a boundary Schwarz lemma for weakly pseudoconvex domains, extending the known strongly pseudoconvex result; the optimal dependence of $m$ on the boundary geometry is not specified.