On minimal 4-folds of general type with <inline-formula><tex-math id="M1">$ p_g \geq 2 $</tex-math></inline-formula>

We show that, for any nonsingular projective 4-fold \begin{document}$ V $\end{document} of general type with geometric genus \begin{document}$ p_g\geq 2 $\end{document} , the pluricanonical map \begin{document}$ \varphi_{33} $\end{document} is birational onto the image and the canonical volume \begin{document}$ {\rm Vol}(V) $\end{document} has the lower bound \begin{document}$ \frac{1}{480} $\end{document} , which improves a previous theorem by Chen and Chen.