Exposing points on the boundary of a strictly pseudoconvex or a locally convexifiable domain of finite 1-type

We show that for any bounded domain $\mathrm{\Omega }\subset {\text{Cp}}^n$ of 1-type $2k$ which is locally convexifiable at $p\in b\mathrm{\Omega }$, having a Stein neighborhood basis, there is a biholomorphic map $f:\bar{\mathrm{\Omega }}\to {\text{Cp}}^n$ such that $f(p)$ is a global extreme point of type $2k$ for $f(\bar{\mathrm{\Omega }})$.