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

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