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Gizatullin surfaces of type $[[0,0,-r_2,-r_3]]$ can be described by theequations $yu = x P(x)$, $xv = u Q(u)$ and $yv = P(x) Q(u)$ in$\mathbb{C}^4_{x,y,u,v}$ where $P$ and $Q$ are non-constant polynomials. Weestablish the algebraic density property for smooth Gizatullin surfaces of thistype. Moreover we also prove the density property for smooth surfaces given bythese equations when $P$ and $Q$ are holomorphic functions.

The density property for Gizatullin surfaces of type $[[0,0,-r_2,-r_3]]$