Greene–Krantz finite-type conjecture for pseudoconvex domains

Let $\Omega$ be a bounded pseudoconvex domain with $C^\infty$ boundary, and let $\mathcal{L}(\Omega)$ denote the limit set of its automorphism group. A point $x\in\mathcal{L}(\Omega)$ is said to have finite type in the sense of Kohn, D'Angelo, or Catlin when it has finite type according to these notions. Greene–Krantz conjecture. If $x\in\mathcal{L}(\Omega)$, then $x$ has finite type in the sense of Kohn/D'Angelo/Catlin. This conjecture concerns the boundary regularity of bounded pseudoconvex domains whose automorphism groups accumulate at $x$; the source presents it as an old conjecture of Greene and Krantz and does not indicate a resolution.